From rrosebru@mta.ca Tue May 1 19:19:52 2001 -0300 Return-Path: Received: (from Majordom@localhost) by mailserv.mta.ca (8.11.1/8.11.1) id f41LdKl11963 for categories-list; Tue, 1 May 2001 18:39:20 -0300 (ADT) X-Authentication-Warning: mailserv.mta.ca: Majordom set sender to cat-dist@mta.ca using -f Date: Mon, 30 Apr 2001 21:37:18 -0700 (PDT) From: Bill Rowan Message-Id: <200105010437.f414bIi14109@transbay.net> To: categories@mta.ca Subject: categories: Abelian Topological Groups Sender: cat-dist@mta.ca Precedence: bulk Status: O X-Status: X-Keywords: X-UID: 1 I am attempting to construct the ideal abelian category within which live complete, hausdorff abelian topological groups. The idea is that the quotients of such a group, in the abelian category, would be completions of the group with respect to topologies coarser than the given one. The subobjects would be those topologies. Of course, having a topology as an object in the abelian category means we have to have objects in the category other than abelian groups. Of course I want to know if this has been done before. Also, what other ideas are there about the ideal abelian category containing these groups? Mac Lane felt that compactly-generated spaces formed the ideal base category for topological algebra. I seem to be using the category of complete, hausdorff uniform spaces as a base category. I wrote a paper on (universal) algebras with a compatible uniformity, and got some nice results about the congruence (actually, uniformity) lattices. But, admittedly, algebras with compatible uniformities have drawbacks as a foundation for topological algebra because even something like the complex numbers cannot be formalized as such, the multiplication not being uniformly continuous. Bill Rowan From rrosebru@mta.ca Wed May 2 13:32:05 2001 -0300 Return-Path: Received: (from Majordom@localhost) by mailserv.mta.ca (8.11.1/8.11.1) id f42Fvi613498 for categories-list; Wed, 2 May 2001 12:57:44 -0300 (ADT) X-Authentication-Warning: mailserv.mta.ca: Majordom set sender to cat-dist@mta.ca using -f X-Authentication-Warning: triples.math.mcgill.ca: barr owned process doing -bs Date: Wed, 2 May 2001 06:11:51 -0400 (EDT) From: Michael Barr X-Sender: barr@triples.math.mcgill.ca To: categories@mta.ca Subject: categories: Re: Abelian Topological Groups In-Reply-To: <200105010437.f414bIi14109@transbay.net> Message-ID: MIME-Version: 1.0 Content-Type: TEXT/PLAIN; charset=US-ASCII Sender: cat-dist@mta.ca Precedence: bulk Status: RO X-Status: X-Keywords: X-UID: 2 One thing is clear: your ideal abelian category is not abelian. Furthermore, you don't get to choose your sub- and quotient objects; they are imposed by the category. Moreover, although a weaker topology (or an abelian group with a weaker topology, which is what I assume is meant) is certainly a subobject, it is not regular, which every subobject in an abelian category must be. In fact, the only abelian categories of topological abelian groups I am aware of are the discrete groups and the dual category of compact groups. For me, the ideal category of topological abelian groups is SP(LCA), the subobjects of products of locally compact abelian groups. It is not abelian, but it is *-autonomous. It is equivalent to the category of weakly topologized abelian groups or SP(R/Z), subobjects of powers of the circle. On Mon, 30 Apr 2001, Bill Rowan wrote: > > I am attempting to construct the ideal abelian category within which live > complete, hausdorff abelian topological groups. The idea is that the > quotients of such a group, in the abelian category, would be completions > of the group with respect to topologies coarser than the given one. The > subobjects would be those topologies. Of course, having a topology as an > object in the abelian category means we have to have objects in the category > other than abelian groups. > > Of course I want to know if this has been done before. Also, what other ideas > are there about the ideal abelian category containing these groups? Mac Lane > felt that compactly-generated spaces formed the ideal base category for > topological algebra. I seem to be using the category of complete, hausdorff > uniform spaces as a base category. I wrote a paper on (universal) algebras > with a compatible uniformity, and got some nice results about the congruence > (actually, uniformity) lattices. But, admittedly, algebras with compatible > uniformities have drawbacks as a foundation for topological algebra because > even something like the complex numbers cannot be formalized as such, the > multiplication not being uniformly continuous. > > Bill Rowan > From rrosebru@mta.ca Wed May 2 13:32:29 2001 -0300 Return-Path: Received: (from Majordom@localhost) by mailserv.mta.ca (8.11.1/8.11.1) id f42Fuim09653 for categories-list; Wed, 2 May 2001 12:56:44 -0300 (ADT) X-Authentication-Warning: mailserv.mta.ca: Majordom set sender to cat-dist@mta.ca using -f Date: Tue, 1 May 2001 16:14:38 -0700 Message-Id: <200105012314.QAA28101@kamiak.eecs.wsu.edu> From: "David Benson" To: categories@mta.ca Subject: categories: Foundational Methods in Computer Science Workshop (FMCS'01) Sender: cat-dist@mta.ca Precedence: bulk Status: RO X-Status: X-Keywords: X-UID: 3 ANNOUNCEMENT Workshop on Foundational Methods in Computer Science -- a series of informal workshops on categories and logic in computer science FMCS'01 : May 31 -- June 3, 2001 Spokane, Washington with sponsorship from the School of Electrical Engineering and Computer Science Washington State University May 31: Arrival day -- Reception in the evening, 7-10pm PDT June 1: Tutorial Talks June 2: Research Talks Conference Banquet June 3: Research Talks in the morning Noon -- end of workshop [includes talks by John MacDonald, Robin Cockett, Ernie Manes, Paul Gilmore, and tutorials by Ernie Manes and Phil Mulry] WORKSHOP HOTEL: WestCoast River Inn (509) 326-5577 (800) 325-4000 State you are with the FMCS conference to obtain the lower conference rate of $US73 per night. [There are a limited number of rooms at this rate, so call soon!] The hotel provides transportation from/to the Spokane airport, so inquire about this when you call... REGISTRATION: Registration information will be forthcoming. As always, the registration fees for students are set at about 60% of non-student registrations and everybody may either prepay or pay onsite. If you plan to attend and have not previously communicated with me, please reply as soon as may be to dbenson@eecs.wsu.edu and indicate if you would like to give a tutorial or a research talk. Thank you! -- Professor David B. Benson (509) 335-2706 School of EE and Computer Science (EME 102A) (509) 335-3818 fax PO Box 642752, Washington State University dbenson@eecs.wsu.edu Pullman WA 99164-2752 U.S.A. From rrosebru@mta.ca Wed May 2 13:34:18 2001 -0300 Return-Path: Received: (from Majordom@localhost) by mailserv.mta.ca (8.11.1/8.11.1) id f42FxPX16742 for categories-list; Wed, 2 May 2001 12:59:25 -0300 (ADT) X-Authentication-Warning: mailserv.mta.ca: Majordom set sender to cat-dist@mta.ca using -f Date: Wed, 2 May 2001 15:04:00 +0200 (CEST) From: Tobias Schroeder X-Sender: tschroed@pc12394 To: Category Mailing List Subject: categories: Limits Message-ID: MIME-Version: 1.0 Content-Type: TEXT/PLAIN; charset=ISO-8859-1 Content-Transfer-Encoding: 8bit X-MIME-Autoconverted: from QUOTED-PRINTABLE to 8bit by mailserv.mta.ca id f42D46b04865 Sender: cat-dist@mta.ca Precedence: bulk Status: O X-Status: X-Keywords: X-UID: 4 Hi, whenever I'm teaching basic category theory, students ask me if there is a connection between limits in the categorical sense and limits in the analytical sense, e.g. the limit of a sequence of real numbers. I've never found an answer to this question. So I'd be very grateful for answers to one of the following: - Can the limit of a sequence of real numbers be expressed as a categorical limit (of course it can if the sequence is monotone, but what if it is not)? - Why have people chosen the term "limit" in category theory? (And, by the way, who has defined it first?) Many thanks in advance Tobias -------------------------------------------------------------- Tobias Schröder FB Mathematik und Informatik Philipps-Universität Marburg WWW: http://www.mathematik.uni-marburg.de/~tschroed email: tschroed@mathematik.uni-marburg.de From rrosebru@mta.ca Wed May 2 13:35:18 2001 -0300 Return-Path: Received: (from Majordom@localhost) by mailserv.mta.ca (8.11.1/8.11.1) id f42FtkC08726 for categories-list; Wed, 2 May 2001 12:55:46 -0300 (ADT) X-Authentication-Warning: mailserv.mta.ca: Majordom set sender to cat-dist@mta.ca using -f Message-ID: <3AEEE88F.1BA9E9BC@cs.uu.nl> Date: Tue, 01 May 2001 18:47:11 +0200 From: Ralf Hinze X-Mailer: Mozilla 4.77 [en] (X11; U; Linux 2.4.0-4GB i686) X-Accept-Language: en MIME-Version: 1.0 To: categories@mta.ca Subject: categories: 2001 Haskell Workshop: final call for papers Content-Type: text/plain; charset=us-ascii Content-Transfer-Encoding: 7bit Sender: cat-dist@mta.ca Precedence: bulk Status: O X-Status: X-Keywords: X-UID: 5 ============================================================================ FINAL CALL FOR PAPERS [Deadline for submission: 1st June 2001] 2001 Haskell Workshop Firenze, Italy, 2nd September 2001 The Haskell Workshop forms part of the PLI 2001 colloquium on Principles, Logics, and Implementations of high-level programming languages, which comprises the ICFP/PPDP conferences and associated workshops. Previous Haskell Workshops have been held in La Jolla (1995), Amsterdam (1997), Paris (1999), and Montreal (2000). http://www.cs.uu.nl/people/ralf/hw2001.{html,pdf,ps,txt} ============================================================================ Scope ----- The purpose of the Haskell Workshop is to discuss experience with Haskell, and possible future developments for the language. The scope of the workshop includes all aspects of the design, semantics, theory, application, implementation, and teaching of Haskell. Submissions that discuss limitations of Haskell at present and/or propose new ideas for future versions of Haskell are particularly encouraged. Adopting an idea from ICFP 2000, the workshop also solicits two special classes of submissions, application letters and functional pearls, described below. Application Letters ------------------- An application letter describes experience using Haskell to solve real-world problems. Such a paper might typically be about six pages, and may be judged by interest of the application and novel use of Haskell. Functional Pearls ----------------- A functional pearl presents - using Haskell as a vehicle - an idea that is small, rounded, and glows with its own light. Such a paper might typically be about six pages, and may be judged by elegance of development and clarity of expression. Submission details ------------------ Deadline for submission: 1st June 2001 Notification of acceptance: 12th July 2001 Final submission due: 1st August 2001 Haskell Workshop: 2nd September 2001 Authors should submit papers in postscript format, formatted for A4 paper, to Ralf Hinze (ralf@cs.uu.nl) by 1st June 2001. Use of the ENTCS style files is strongly recommended. The length should be restricted to the equivalent of 5000 words (which is approximately 24 pages in ENTCS format, or 12 pages in ACM format). Note that this word limit represents a change from the first call for papers. Application letters and functional pearls should be labeled as such on the first page; they may be any length up to the above limit, though shorter submissions are welcome. The accepted papers will initially appear as a University of Utrecht technical report, and subsequently be published as an issue of Electronic Notes in Theoretical Computer Science. Programme committee ------------------- Manuel Chakravarty University of New South Wales Jeremy Gibbons University of Oxford Ralf Hinze (chair) University of Utrecht Patrik Jansson Chalmers University Mark Jones Oregon Graduate Institute Ross Paterson City University, London Simon Peyton Jones Microsoft Research Stephanie Weirich Cornell University ============================================================================ From rrosebru@mta.ca Wed May 2 13:36:05 2001 -0300 Return-Path: Received: (from Majordom@localhost) by mailserv.mta.ca (8.11.1/8.11.1) id f42FwRv24840 for categories-list; Wed, 2 May 2001 12:58:27 -0300 (ADT) X-Authentication-Warning: mailserv.mta.ca: Majordom set sender to cat-dist@mta.ca using -f X-Authentication-Warning: triples.math.mcgill.ca: barr owned process doing -bs Date: Wed, 2 May 2001 06:34:23 -0400 (EDT) From: Michael Barr X-Sender: barr@triples.math.mcgill.ca To: Categories list Subject: categories: diagxy.tex, final version Message-ID: MIME-Version: 1.0 Content-Type: TEXT/PLAIN; charset=US-ASCII Sender: cat-dist@mta.ca Precedence: bulk Status: O X-Status: X-Keywords: X-UID: 6 % This is a package of commutative diagram macros built on top of Xy-pic % by Michael Barr (email: barr@barrs.org). This may be freely % distributed, unchanged, for non-commercial or commercial use. If % changed, it must be renamed. Inclusion in a commercial software package % is also permitted, provided I receive one free copy of the software % package for my personal use. There are no guarantees that this package % is good for anything. I have tested it with LaTeX 2e, LaTeX 2.09 and % Plain TeX. Although I know of no reason it will not work with AMSTeX, I % have not tested it. \input xy \xyoption{arrow} \newdir{ >}{{ }*!/-9pt/@{>}} \newdir{ (}{{ }*!/-5pt/@{(}} \newdir^{ (}{{ }*!/-5pt/@^{(}} \newdir{< }{!/9pt/@{<}*{ }} \newbox\Label% \newdimen\high% \newdimen\deep% \newdimen\ul% \newcount\deltax% \newcount\deltay% \newcount\deltaX% \newcount\deltaY% \newdimen\wdth \newcount\xend% \newcount\yend% \newcount\Xend \newcount\Yend \newcount\xpos% \newcount\ypos% \newcount\default \default=500% \newcount\defaultmargin \defaultmargin=200% \newcount\topw% \newcount\botw% \newcount\Xpos% \newcount\Ypos% \def\ratchet#1#2{\ifnum#1<#2\global #1=#2\fi}% \newcount\atcode \atcode=\catcode`\@% \catcode`\@=11 \expandafter\ifx\csname @ifnextchar\endcsname\relax \def\ifnextchar#1#2#3{\let\@tempe #1\def\@tempa{#2}\def\@tempb{#3}\futurelet \@tempc\@ifnch} \def\@ifnch{\ifx \@tempc \@sptoken \let\@tempd\@xifnch \else \ifx \@tempc \@tempe\let\@tempd\@tempa\else\let\@tempd\@tempb\fi \fi \@tempd} \def\:{\let\@sptoken= } \: % this makes \@sptoken a space token \def\:{\@xifnch} \expandafter\def\: {\futurelet\@tempc\@ifnch} \else \let\ifnextchar\@ifnextchar \fi \ul=.01em% \X@xbase =.01em% \Y@ybase =.01em% \def\scalefactor#1{\ul=#1\ul \X@xbase=#1\X@xbase \Y@ybase=#1\Y@ybase}% \catcode`\@=12% \let\bfig\xy% \let\efig\endxy% \def\car#1#2\nil{#1}% \def\morphism{\ifnextchar({\morphismp}{\morphismp(0,0)}}% \def\morphismp(#1){\ifnextchar|{\morphismpp(#1)}{\morphismpp(#1)|a|}}% \def\morphismpp(#1)|#2|{\ifnextchar/{\morphismppp(#1)|#2|}% {\morphismppp(#1)|#2|/>/}}% \def\morphismppp(#1)|#2|/#3/{% \ifnextchar<{\morphismpppp(#1)|#2|/#3/}% {\morphismpppp(#1)|#2|/#3/<\default,0>}}% \def\morphismpppp(#1,#2)|#3|/#4/<#5,#6>[#7`#8;#9]{% \xend#1\advance \xend by #5% \yend#2\advance \yend by #6% \domorphism(#1,#2)|#3|/#4/<#5,#6>[#7`#8;#9]} \def\domorphism(#1,#2)|#3|/#4/<#5,#6>[#7`#8;#9]{% \edef\next{#4}% \ifx\next\empty \POS(#1,#2)*+{#7}\ar@{} (\xend,\yend)*+{#8}% \else \def\next{\car#4\nil}\fi \if@\next\relax \if#3l% \ifnum #6>0% \POS(#1,#2)*+{#7}\ar#4^-{#9} (\xend,\yend)*+{#8}% \else% \POS(#1,#2)*+{#7}\ar#4_-{#9} (\xend,\yend)*+{#8}% \fi% \else \if#3m% \edef\next{#9}% \ifx\next\empty \POS(#1,#2)*+{#7}\ar#4 (\xend,\yend)*+{#8}% \else \setbox\Label=\hbox{\kern .5pt $\labelstyle #9$\kern .5pt}% \high=\ht\Label \advance\high by 1pt \ht\Label=\high% \deep=\dp\Label \advance\deep by 1pt \dp\Label=\deep% \POS(#1,#2)*+{#7}\ar#4|-{\box\Label} (\xend,\yend)*+{#8}% \fi \else \if#3r% \ifnum #6<0% \POS(#1,#2)*+{#7}\ar#4^-{#9} (\xend,\yend)*+{#8}% \else% \POS(#1,#2)*+{#7}\ar#4_-{#9} (\xend,\yend)*+{#8}% \fi% \else \if#3a% \ifnum #5>0% \POS(#1,#2)*+{#7}\ar#4^-{#9} (\xend,\yend)*+{#8}% \else% \POS(#1,#2)*+{#7}\ar#4_-{#9} (\xend,\yend)*+{#8}% \fi% \else \if#3b% \ifnum #5<0% \POS(#1,#2)*+{#7}\ar#4^-{#9} (\xend,\yend)*+{#8}% \else% \POS(#1,#2)*+{#7}\ar#4_-{#9} (\xend,\yend)*+{#8}% \fi% \else \POS(#1,#2)*+{#7}\ar#4 (\xend,\yend)*+{#8}% \fi\fi\fi\fi\fi% \else% \edef\next{#4}% \ifx\next\empty% \POS(#1,#2)*+{#7}; (\xend,\yend)*+{#8}% \else \edef\next{#4}% \ifx\next\empty% \POS(#1,#2)*+{#7}\ar (\xend,\yend)*+{#8}% \else \if#3l% \ifnum #6>0% \POS(#1,#2)*+{#7}\ar@{#4}^-{#9} (\xend,\yend)*+{#8}% \else% \POS(#1,#2)*+{#7}\ar@{#4}_-{#9} (\xend,\yend)*+{#8}% \fi% \else \if#3m% \edef\next{#9}% \ifx\next\empty \POS(#1,#2)*+{#7}\ar@{#4} (\xend,\yend)*+{#8}% \else \setbox\Label=\hbox{\kern .5pt $\labelstyle #9$\kern .5pt}% \high=\ht\Label \advance\high by 1pt \ht\Label=\high% \deep=\dp\Label \advance\deep by 1pt \dp\Label=\deep% \POS(#1,#2)*+{#7}\ar@{#4}|-{\box\Label} (\xend,\yend)*+{#8}% \fi \else \if#3r% \ifnum #6<0% \POS(#1,#2)*+{#7}\ar@{#4}^-{#9} (\xend,\yend)*+{#8}% \else% \POS(#1,#2)*+{#7}\ar@{#4}_-{#9} (\xend,\yend)*+{#8}% \fi% \else \if#3a% \ifnum #5>0% \POS(#1,#2)*+{#7}\ar@{#4}^-{#9} (\xend,\yend)*+{#8}% \else% \POS(#1,#2)*+{#7}\ar@{#4}_-{#9} (\xend,\yend)*+{#8}% \fi% \else \if#3b% \ifnum #5<0% \POS(#1,#2)*+{#7}\ar@{#4}^-{#9} (\xend,\yend)*+{#8}% \else% \POS(#1,#2)*+{#7}\ar@{#4}_-{#9} (\xend,\yend)*+{#8}% \fi% \else \POS(#1,#2)*+{#7}\ar@{#4} (\xend,\yend)*+{#8}% \fi\fi\fi\fi\fi\fi\fi% \fi\ignorespaces}% \def\squarepppp(#1,#2)|#3|/#4`#5`#6`#7/<#8>[#9]{% \xpos#1\ypos#2% \def\next|##1##2##3##4|{% \def\xa{##1}\def\xb{##2}\def\xc{##3}\def\xd{##4}\ignorespaces}% \next|#3|% \def\next<##1,##2>{\deltax=##1\deltay=##2\ignorespaces}% \next<#8>% \def\next[##1`##2`##3`##4;##5`##6`##7`##8]{% \def\nodea{##1}\def\nodeb{##2}\def\nodec{##3}\def\noded{##4}% \def\labela{##5}\def\labelb{##6}\def\labelc{##7}\def\labeld{##8}\ignorespaces}% \next[#9]% \morphism(\xpos,\ypos)|\xd|/#7/<\deltax,0>[\nodec`\noded;\labeld]% \advance \ypos by \deltay% \morphism(\xpos,\ypos)|\xb|/#5/<0,-\deltay>[\nodea`\nodec;\labelb]% \morphism(\xpos,\ypos)|\xa|/#4/<\deltax,0>[\nodea`\nodeb;\labela]% \advance \xpos by \deltax% \morphism(\xpos,\ypos)|\xc|/#6/<0,-\deltay>[\nodeb`\noded;\labelc]% \ignorespaces}% \def\square{\ifnextchar({\squarep}{\squarep(0,0)}}% \def\squarep(#1){\ifnextchar|{\squarepp(#1)}{\squarepp(#1)|alrb|}}% \def\squarepp(#1)|#2|{\ifnextchar/{\squareppp(#1)|#2|}% {\squareppp(#1)|#2|/>`>`>`>/}}% \def\squareppp(#1)|#2|/#3`#4`#5`#6/{% \ifnextchar<{\squarepppp(#1)|#2|/#3`#4`#5`#6/}% {\squarepppp(#1)|#2|/#3`#4`#5`#6/<\default,\default>}}% \def\ptrianglepppp(#1,#2)|#3|/#4`#5`#6/<#7>[#8]{% \xpos#1\ypos#2% \def\next|##1##2##3|{\def\xa{##1}\def\xb{##2}\def\xc{##3}}% \next|#3|% \def\next<##1,##2>{\deltax=##1\deltay=##2\ignorespaces}% \next<#7>% \def\next[##1`##2`##3;##4`##5`##6]{% \def\nodea{##1}\def\nodeb{##2}\def\nodec{##3}% \def\labela{##4}\def\labelb{##5}\def\labelc{##6}}% \next[#8]% \advance\ypos by \deltay% \morphism(\xpos,\ypos)|\xa|/#4/<\deltax,0>[\nodea`\nodeb;\labela]% \morphism(\xpos,\ypos)|\xb|/#5/<0,-\deltay>[\nodea`\nodec;\labelb]% \advance\xpos by \deltax% \morphism(\xpos,\ypos)|\xc|/#6/<-\deltax,-\deltay>[\nodeb`\nodec;\labelc]% \ignorespaces}% \def\qtrianglepppp(#1,#2)|#3|/#4`#5`#6/<#7>[#8]{% \xpos#1\ypos#2% \def\next|##1##2##3|{\def\xa{##1}\def\xb{##2}\def\xc{##3}}% \next|#3|% \def\next<##1,##2>{\deltax=##1\deltay=##2\ignorespaces}% \next<#7>% \def\next[##1`##2`##3;##4`##5`##6]{% \def\nodea{##1}\def\nodeb{##2}\def\nodec{##3}% \def\labela{##4}\def\labelb{##5}\def\labelc{##6}}% \next[#8]% \advance\ypos by \deltay% \morphism(\xpos,\ypos)|\xa|/#4/<\deltax,0>[\nodea`\nodeb;\labela]% \morphism(\xpos,\ypos)|\xb|/#5/<\deltax,-\deltay>[\nodea`\nodec;\labelb]% \advance\xpos by \deltax% \morphism(\xpos,\ypos)|\xc|/#6/<0,-\deltay>[\nodeb`\nodec;\labelc]% \ignorespaces}% \def\dtrianglepppp(#1,#2)|#3|/#4`#5`#6/<#7>[#8]{% \xpos#1\ypos#2% \def\next|##1##2##3|{\def\xa{##1}\def\xb{##2}\def\xc{##3}}% \next|#3|% \def\next<##1,##2>{\deltax=##1\deltay=##2\ignorespaces}% \next<#7>% \def\next[##1`##2`##3;##4`##5`##6]{% \def\nodea{##1}\def\nodeb{##2}\def\nodec{##3}% \def\labela{##4}\def\labelb{##5}\def\labelc{##6}}% \next[#8]% \morphism(\xpos,\ypos)|\xc|/#6/<\deltax,0>[\nodeb`\nodec;\labelc]% \advance\ypos by \deltay\advance \xpos by \deltax% \morphism(\xpos,\ypos)|\xa|/#4/<-\deltax,-\deltay>[\nodea`\nodeb;\labela]% \morphism(\xpos,\ypos)|\xb|/#5/<0,-\deltay>[\nodea`\nodec;\labelb]% \ignorespaces}% \def\btrianglepppp(#1,#2)|#3|/#4`#5`#6/<#7>[#8]{% \xpos#1\ypos#2% \def\next|##1##2##3|{\def\xa{##1}\def\xb{##2}\def\xc{##3}}% \next|#3|% \def\next<##1,##2>{\deltax=##1\deltay=##2\ignorespaces}% \next<#7>% \def\next[##1`##2`##3;##4`##5`##6]{% \def\nodea{##1}\def\nodeb{##2}\def\nodec{##3}% \def\labela{##4}\def\labelb{##5}\def\labelc{##6}}% \next[#8]% \morphism(\xpos,\ypos)|\xc|/#6/<\deltax,0>[\nodeb`\nodec;\labelc]% \advance\ypos by \deltay% \morphism(\xpos,\ypos)|\xa|/#4/<0,-\deltay>[\nodea`\nodeb;\labela]% \morphism(\xpos,\ypos)|\xb|/#5/<\deltax,-\deltay>[\nodea`\nodec;\labelb]% \ignorespaces}% \def\Atrianglepppp(#1,#2)|#3|/#4`#5`#6/<#7>[#8]{% \xpos#1\ypos#2% \def\next|##1##2##3|{\def\xa{##1}\def\xb{##2}\def\xc{##3}}% \next|#3|% \def\next<##1,##2>{\deltax=##1\deltay=##2\ignorespaces}% \next<#7>% \def\next[##1`##2`##3;##4`##5`##6]{% \def\nodea{##1}\def\nodeb{##2}\def\nodec{##3}% \def\labela{##4}\def\labelb{##5}\def\labelc{##6}}% \next[#8]% \multiply\deltax by 2% \morphism(\xpos,\ypos)|\xc|/#6/<\deltax,0>[\nodeb`\nodec;\labelc]% \divide\deltax by 2 \advance\ypos by \deltay\advance\xpos by \deltax% \morphism(\xpos,\ypos)|\xa|/#4/<-\deltax,-\deltay>[\nodea`\nodeb;\labela]% \morphism(\xpos,\ypos)|\xb|/#5/<\deltax,-\deltay>[\nodea`\nodec;\labelb]% \ignorespaces}% \def\Vtrianglepppp(#1,#2)|#3|/#4`#5`#6/<#7>[#8]{% \xpos#1\ypos#2% \def\next|##1##2##3|{\def\xa{##1}\def\xb{##2}\def\xc{##3}}% \next|#3|% \def\next<##1,##2>{\deltax=##1\deltay=##2\ignorespaces}% \next<#7>% \def\next[##1`##2`##3;##4`##5`##6]{% \def\nodea{##1}\def\nodeb{##2}\def\nodec{##3}% \def\labela{##4}\def\labelb{##5}\def\labelc{##6}}% \next[#8]% \advance\ypos by \deltay% \morphism(\xpos,\ypos)|\xb|/#5/<\deltax,-\deltay>[\nodea`\nodec;\labelb]% \multiply\deltax by 2% \morphism(\xpos,\ypos)|\xa|/#4/<\deltax,0>[\nodea`\nodeb;\labela]% \advance\xpos by \deltax \divide \deltax by 2 \morphism(\xpos,\ypos)|\xc|/#6/<-\deltax,-\deltay>[\nodeb`\nodec;\labelc]% \ignorespaces}% \def\Ctrianglepppp(#1,#2)|#3|/#4`#5`#6/<#7>[#8]{% \xpos#1\ypos#2% \def\next|##1##2##3|{\def\xa{##1}\def\xb{##2}\def\xc{##3}}% \next|#3|% \def\next<##1,##2>{\deltax=##1\deltay=##2\ignorespaces}% \next<#7>% \def\next[##1`##2`##3;##4`##5`##6]{% \def\nodea{##1}\def\nodeb{##2}\def\nodec{##3}% \def\labela{##4}\def\labelb{##5}\def\labelc{##6}}% \next[#8]% \advance \ypos by \deltay% \morphism(\xpos,\ypos)|\xc|/#6/<\deltax,-\deltay>[\nodeb`\nodec;\labelc]% \advance\ypos by \deltay \advance \xpos by \deltax% \morphism(\xpos,\ypos)|\xa|/#4/<-\deltax,-\deltay>[\nodea`\nodeb;\labela]% \multiply\deltay by 2% \morphism(\xpos,\ypos)|\xb|/#5/<0,-\deltay>[\nodea`\nodec;\labelb]% \ignorespaces}% \def\Dtrianglepppp(#1,#2)|#3|/#4`#5`#6/<#7>[#8]{% \xpos#1\ypos#2% \def\next|##1##2##3|{\def\xa{##1}\def\xb{##2}\def\xc{##3}}% \next|#3|% \def\next<##1,##2>{\deltax=##1\deltay=##2\ignorespaces}% \next<#7>% \def\next[##1`##2`##3;##4`##5`##6]{% \def\nodea{##1}\def\nodeb{##2}\def\nodec{##3}% \def\labela{##4}\def\labelb{##5}\def\labelc{##6}}% \next[#8]% \advance\xpos by \deltax \advance\ypos by \deltay% \morphism(\xpos,\ypos)|\xc|/#6/<-\deltax,-\deltay>[\nodeb`\nodec;\labelc]% \advance\xpos by -\deltax \advance\ypos by \deltay% \morphism(\xpos,\ypos)|\xb|/#5/<\deltax,-\deltay>[\nodea`\nodeb;\labelb]% \multiply \deltay by 2% \morphism(\xpos,\ypos)|\xa|/#4/<0,-\deltay>[\nodea`\nodec;\labela]% \ignorespaces}% \def\ptriangle{\ifnextchar({\ptrianglep}{\ptrianglep(0,0)}}% \def\ptrianglep(#1){\ifnextchar|{\ptrianglepp(#1)}{\ptrianglepp(#1)|alr|}}% \def\ptrianglepp(#1)|#2|{\ifnextchar/{\ptriangleppp(#1)|#2|}% {\ptriangleppp(#1)|#2|/>`>`>/}}% \def\ptriangleppp(#1)|#2|/#3`#4`#5/{% \ifnextchar<{\ptrianglepppp(#1)|#2|/#3`#4`#5/}% {\ptrianglepppp(#1)|#2|/#3`#4`#5/<\default,\default>}}% \def\qtriangle{\ifnextchar({\qtrianglep}{\qtrianglep(0,0)}}% \def\qtrianglep(#1){\ifnextchar|{\qtrianglepp(#1)}{\qtrianglepp(#1)|alr|}}% \def\qtrianglepp(#1)|#2|{\ifnextchar/{\qtriangleppp(#1)|#2|}% {\qtriangleppp(#1)|#2|/>`>`>/}}% \def\qtriangleppp(#1)|#2|/#3`#4`#5/{% \ifnextchar<{\qtrianglepppp(#1)|#2|/#3`#4`#5/}% {\qtrianglepppp(#1)|#2|/#3`#4`#5/<\default,\default>}}% \def\dtriangle{\ifnextchar({\dtrianglep}{\dtrianglep(0,0)}}% \def\dtrianglep(#1){\ifnextchar|{\dtrianglepp(#1)}{\dtrianglepp(#1)|lrb|}}% \def\dtrianglepp(#1)|#2|{\ifnextchar/{\dtriangleppp(#1)|#2|}% {\dtriangleppp(#1)|#2|/>`>`>/}}% \def\dtriangleppp(#1)|#2|/#3`#4`#5/{% \ifnextchar<{\dtrianglepppp(#1)|#2|/#3`#4`#5/}% {\dtrianglepppp(#1)|#2|/#3`#4`#5/<\default,\default>}}% \def\btriangle{\ifnextchar({\btrianglep}{\btrianglep(0,0)}}% \def\btrianglep(#1){\ifnextchar|{\btrianglepp(#1)}{\btrianglepp(#1)|lrb|}}% \def\btrianglepp(#1)|#2|{\ifnextchar/{\btriangleppp(#1)|#2|}% {\btriangleppp(#1)|#2|/>`>`>/}}% \def\btriangleppp(#1)|#2|/#3`#4`#5/{% \ifnextchar<{\btrianglepppp(#1)|#2|/#3`#4`#5/}% {\btrianglepppp(#1)|#2|/#3`#4`#5/<\default,\default>}}% \def\Atriangle{\ifnextchar({\Atrianglep}{\Atrianglep(0,0)}}% \def\Atrianglep(#1){\ifnextchar|{\Atrianglepp(#1)}{\Atrianglepp(#1)|lrb|}}% \def\Atrianglepp(#1)|#2|{\ifnextchar/{\Atriangleppp(#1)|#2|}% {\Atriangleppp(#1)|#2|/>`>`>/}}% \def\Atriangleppp(#1)|#2|/#3`#4`#5/{% \ifnextchar<{\Atrianglepppp(#1)|#2|/#3`#4`#5/}% {\Atrianglepppp(#1)|#2|/#3`#4`#5/<\default,\default>}}% \def\Vtriangle{\ifnextchar({\Vtrianglep}{\Vtrianglep(0,0)}}% \def\Vtrianglep(#1){\ifnextchar|{\Vtrianglepp(#1)}{\Vtrianglepp(#1)|alb|}}% \def\Vtrianglepp(#1)|#2|{\ifnextchar/{\Vtriangleppp(#1)|#2|}% {\Vtriangleppp(#1)|#2|/>`>`>/}}% \def\Vtriangleppp(#1)|#2|/#3`#4`#5/{% \ifnextchar<{\Vtrianglepppp(#1)|#2|/#3`#4`#5/}% {\Vtrianglepppp(#1)|#2|/#3`#4`#5/<\default,\default>}}% \def\Ctriangle{\ifnextchar({\Ctrianglep}{\Ctrianglep(0,0)}}% \def\Ctrianglep(#1){\ifnextchar|{\Ctrianglepp(#1)}{\Ctrianglepp(#1)|arb|}}% \def\Ctrianglepp(#1)|#2|{\ifnextchar/{\Ctriangleppp(#1)|#2|}% {\Ctriangleppp(#1)|#2|/>`>`>/}}% \def\Ctriangleppp(#1)|#2|/#3`#4`#5/{% \ifnextchar<{\Ctrianglepppp(#1)|#2|/#3`#4`#5/}% {\Ctrianglepppp(#1)|#2|/#3`#4`#5/<\default,\default>}}% \def\Dtriangle{\ifnextchar({\Dtrianglep}{\Dtrianglep(0,0)}}% \def\Dtrianglep(#1){\ifnextchar|{\Dtrianglepp(#1)}{\Dtrianglepp(#1)|alb|}}% \def\Dtrianglepp(#1)|#2|{\ifnextchar/{\Dtriangleppp(#1)|#2|}% {\Dtriangleppp(#1)|#2|/>`>`>/}}% \def\Dtriangleppp(#1)|#2|/#3`#4`#5/{% \ifnextchar<{\Dtrianglepppp(#1)|#2|/#3`#4`#5/}% {\Dtrianglepppp(#1)|#2|/#3`#4`#5/<\default,\default>}}% \def\Atrianglepairpppp(#1)|#2|/#3`#4`#5`#6`#7/<#8>[#9]{% \def\next(##1,##2){\xpos##1\ypos##2} \next(#1)% \def\next|##1##2##3##4##5|{\def\xa{##1}\def\xb{##2}% \def\xc{##3}\def\xd{##4}\def\xe{##5}}% \next|#2| \def\next<##1,##2>{\deltax=##1\deltay=##2\ignorespaces}% \next<#8>% \def\next[##1`##2`##3`##4;##5`##6`##7`##8`##9]{% \def\nodea{##1}\def\nodeb{##2}\def\nodec{##3}\def\noded{##4}% \def\labela{##5}\def\labelb{##6}\def\labelc{##7}\def\labeld{##8}\def\labele{##9}}% \next[#9]% \morphism(\xpos,\ypos)|\xd|/#6/<\deltax,0>[\nodeb`\nodec;\labeld]% \advance\xpos by \deltax% \morphism(\xpos,\ypos)|\xe|/#7/<\deltax,0>[\nodec`\noded;\labele]% \advance\ypos by \deltay% \morphism(\xpos,\ypos)|\xa|/#3/<-\deltax,-\deltay>[\nodea`\nodeb;\labela]% \morphism(\xpos,\ypos)|\xb|/#4/<0,-\deltay>[\nodea`\nodec;\labelb]% \morphism(\xpos,\ypos)|\xc|/#5/<\deltax,-\deltay>[\nodea`\noded;\labelc]% \ignorespaces}% \def\Vtrianglepairpppp(#1)|#2|/#3`#4`#5`#6`#7/<#8>[#9]{% \def\next(##1,##2){\xpos##1\ypos##2} \next(#1)% \def\next|##1##2##3##4##5|{\def\xa{##1}\def\xb{##2}% \def\xc{##3}\def\xd{##4}\def\xe{##5}}% \next|#2| \def\next<##1,##2>{\deltax=##1\deltay=##2\ignorespaces}% \next<#8>% \def\next[##1`##2`##3`##4;##5`##6`##7`##8`##9]{% \def\nodea{##1}\def\nodeb{##2}\def\nodec{##3}\def\noded{##4}% \def\labela{##5}\def\labelb{##6}\def\labelc{##7}\def\labeld{##8}\def\labele{##9}}% \next[#9]% \advance\ypos by \deltay% \morphism(\xpos,\ypos)|\xa|/#3/<\deltax,0>[\nodea`\nodeb;\labela]% \morphism(\xpos,\ypos)|\xc|/#5/<\deltax,-\deltay>[\nodea`\noded;\labelc]% \advance\xpos by \deltax% \morphism(\xpos,\ypos)|\xb|/#4/<\deltax,0>[\nodeb`\nodec;\labelb]% \morphism(\xpos,\ypos)|\xd|/#6/<0,-\deltay>[\nodeb`\noded;\labeld]% \advance\xpos by \deltax% \morphism(\xpos,\ypos)|\xe|/#7/<-\deltax,-\deltay>[\nodec`\noded;\labele]% \ignorespaces}% \def\Ctrianglepairpppp(#1)|#2|/#3`#4`#5`#6`#7/<#8>[#9]{% \def\next(##1,##2){\xpos##1\ypos##2} \next(#1)% \def\next|##1##2##3##4##5|{\def\xa{##1}\def\xb{##2}% \def\xc{##3}\def\xd{##4}\def\xe{##5}}% \next|#2| \def\next<##1,##2>{\deltax=##1\deltay=##2\ignorespaces}% \next<#8>% \def\next[##1`##2`##3`##4;##5`##6`##7`##8`##9]{% \def\nodea{##1}\def\nodeb{##2}\def\nodec{##3}\def\noded{##4}% \def\labela{##5}\def\labelb{##6}\def\labelc{##7}\def\labeld{##8}\def\labele{##9}}% \next[#9]% \advance\ypos by \deltay% \morphism(\xpos,\ypos)|\xe|/#7/<0,-\deltay>[\nodec`\noded;\labele]% \advance\xpos by -\deltax% \morphism(\xpos,\ypos)|\xc|/#5/<\deltax,0>[\nodeb`\nodec;\labelc]% \morphism(\xpos,\ypos)|\xd|/#6/<\deltax,-\deltay>[\nodeb`\noded;\labeld]% \advance\ypos by \deltay% \advance\xpos by \deltax% \morphism(\xpos,\ypos)|\xa|/#3/<-\deltax,-\deltay>[\nodea`\nodeb;\labela]% \morphism(\xpos,\ypos)|\xb|/#4/<0,-\deltay>[\nodea`\nodec;\labelb]% \ignorespaces}% \def\Dtrianglepairpppp(#1)|#2|/#3`#4`#5`#6`#7/<#8>[#9]{% \def\next(##1,##2){\xpos##1\ypos##2} \next(#1)% \def\next|##1##2##3##4##5|{\def\xa{##1}\def\xb{##2}% \def\xc{##3}\def\xd{##4}\def\xe{##5}}% \next|#2| \def\next<##1,##2>{\deltax=##1\deltay=##2\ignorespaces}% \next<#8>% \def\next[##1`##2`##3`##4;##5`##6`##7`##8`##9]{% \def\nodea{##1}\def\nodeb{##2}\def\nodec{##3}\def\noded{##4}% \def\labela{##5}\def\labelb{##6}\def\labelc{##7}\def\labeld{##8}\def\labele{##9}}% \next[#9]% \advance\ypos by \deltay% \morphism(\xpos,\ypos)|\xc|/#5/<\deltax,0>[\nodeb`\nodec;\labelc]% \morphism(\xpos,\ypos)|\xd|/#6/<0,-\deltay>[\nodeb`\noded;\labeld]% \advance\ypos by \deltay% \morphism(\xpos,\ypos)|\xa|/#3/<0,-\deltay>[\nodea`\nodeb;\labela]% \morphism(\xpos,\ypos)|\xb|/#4/<\deltax,-\deltay>[\nodea`\nodec;\labelb]% \advance\ypos by -\deltay% \advance\xpos by \deltax% \morphism(\xpos,\ypos)|\xe|/#7/<-\deltax,-\deltay>[\nodec`\noded;\labele]% \ignorespaces}% \def\Atrianglepair{\ifnextchar({\Atrianglepairp}{\Atrianglepairp(0,0)}}% \def\Atrianglepairp(#1){\ifnextchar|{\Atrianglepairpp(#1)}% {\Atrianglepairpp(#1)|lmrbb|}}% \def\Atrianglepairpp(#1)|#2|{\ifnextchar/{\Atrianglepairppp(#1)|#2|}% {\Atrianglepairppp(#1)|#2|/>`>`>`>`>/}}% \def\Atrianglepairppp(#1)|#2|/#3`#4`#5`#6`#7/{% \ifnextchar<{\Atrianglepairpppp(#1)|#2|/#3`#4`#5`#6`#7/}% {\Atrianglepairpppp(#1)|#2|/#3`#4`#5`#6`#7/<\default,\default>}}% \def\Vtrianglepair{\ifnextchar({\Vtrianglepairp}{\Vtrianglepairp(0,0)}}% \def\Vtrianglepairp(#1){\ifnextchar|{\Vtrianglepairpp(#1)}% {\Vtrianglepairpp(#1)|aalmr|}}% \def\Vtrianglepairpp(#1)|#2|{\ifnextchar/{\Vtrianglepairppp(#1)|#2|}% {\Vtrianglepairppp(#1)|#2|/>`>`>`>`>/}}% \def\Vtrianglepairppp(#1)|#2|/#3`#4`#5`#6`#7/{% \ifnextchar<{\Vtrianglepairpppp(#1)|#2|/#3`#4`#5`#6`#7/}% {\Vtrianglepairpppp(#1)|#2|/#3`#4`#5`#6`#7/<\default,\default>}}% \def\Ctrianglepair{\ifnextchar({\Ctrianglepairp}{\Ctrianglepairp(0,0)}}% \def\Ctrianglepairp(#1){\ifnextchar|{\Ctrianglepairpp(#1)}% {\Ctrianglepairpp(#1)|lrmlr|}}% \def\Ctrianglepairpp(#1)|#2|{\ifnextchar/{\Ctrianglepairppp(#1)|#2|}% {\Ctrianglepairppp(#1)|#2|/>`>`>`>`>/}}% \def\Ctrianglepairppp(#1)|#2|/#3`#4`#5`#6`#7/{% \ifnextchar<{\Ctrianglepairpppp(#1)|#2|/#3`#4`#5`#6`#7/}% {\Ctrianglepairpppp(#1)|#2|/#3`#4`#5`#6`#7/<\default,\default>}}% \def\Dtrianglepair{\ifnextchar({\Dtrianglepairp}{\Dtrianglepairp(0,0)}}% \def\Dtrianglepairp(#1){\ifnextchar|{\Dtrianglepairpp(#1)}% {\Dtrianglepairpp(#1)|lrmlr|}}% \def\Dtrianglepairpp(#1)|#2|{\ifnextchar/{\Dtrianglepairppp(#1)|#2|}% {\Dtrianglepairppp(#1)|#2|/>`>`>`>`>/}}% \def\Dtrianglepairppp(#1)|#2|/#3`#4`#5`#6`#7/{% \ifnextchar<{\Dtrianglepairpppp(#1)|#2|/#3`#4`#5`#6`#7/}% {\Dtrianglepairpppp(#1)|#2|/#3`#4`#5`#6`#7/<\default,\default>}}% \def\place(#1,#2)[#3]{\POS(#1,#2)*+{#3}}% \def\pullback#1]#2]{\square#1]\trident#2]}% \def\tridentppp|#1#2#3|/#4`#5`#6/<#7,#8>[#9]{% \def\next[##1;##2`##3`##4]{\def\nodee{##1}\def\labele{##2}% \def\labelf{##3}\def\labelg{##4}}% \next[#9]% \advance \xpos by -\deltax% \advance \xpos by -#7\advance \ypos by #8% \advance\deltax by #7% \morphism(\xpos,\ypos)|#1|/#4/<\deltax,-#8>[\nodee`\nodeb;\labele]% \advance\deltax by -#7% \morphism(\xpos,\ypos)|#2|/#5/<#7,-#8>[\nodee`\nodea;\labelf]% \advance\deltay by #8% \morphism(\xpos,\ypos)|#3|/#6/<#7,-\deltay>[\nodee`\nodec;\labelg]% \ignorespaces}% \def\trident{\ifnextchar|{\tridentp}{\tridentp|amb|}}% \def\tridentp|#1|{\ifnextchar/{\tridentpp|#1|}{\tridentpp|#1|/{>}`{>}`{>}/}}% \def\tridentpp|#1|/#2/{\ifnextchar<{\tridentppp|#1|/#2/}% {\tridentppp|#1|/#2/<500,500>}}% \def\setmorphismwidth#1#2#3#4{% \setbox0=\hbox{$#1#3#3#2$}#4=\wd0% \divide #4 by 2 \divide #4 by \ul% \advance #4 by \defaultmargin \ratchet{#4}{500}}% \def\setSquarewidth[#1`#2`#3`#4;#5`#6`#7`#8]{% \setmorphismwidth{#1}{#2}{#5}{\topw}% \setmorphismwidth{#3}{#4}{#8}{\botw}% \ratchet{\topw}{\botw}}% \def\Squarepppp(#1)|#2|/#3/<#4>[#5]{% \setSquarewidth[#5]% \squarepppp(#1)|#2|/#3/<\topw,#4>[#5]% \ignorespaces}% \def\Square{\ifnextchar({\Squarep}{\Squarep(0,0)}}% \def\Squarep(#1){\ifnextchar|{\Squarepp(#1)}{\Squarepp(#1)|alrb|}}% \def\Squarepp(#1)|#2|{\ifnextchar/{\Squareppp(#1)|#2|}% {\Squareppp(#1)|#2|/>`>`>`>/}}% \def\Squareppp(#1)|#2|/#3`#4`#5`#6/{% \ifnextchar<{\Squarepppp(#1)|#2|/#3`#4`#5`#6/}% {\Squarepppp(#1)|#2|/#3`#4`#5`#6/<\default>}}% \def\hSquarespppp(#1,#2)|#3|/#4/<#5>[#6;#7]{% \Xpos=#1\Ypos=#2% \def\next|##1`##2`##3`##4`##5`##6`##7|{% \def\Xa{##1}\def\Xb{##2}\def\Xc{##3}\def\Xd{##4}% \def\Xe{##5}\def\Xf{##6}\def\Xg{##7}}% \next|#3|% \deltaY=#5% \def\next[##1`##2`##3`##4`##5`##6]{% \def\Nodea{##1}\def\Nodeb{##2}\def\Nodec{##3}% \def\Noded{##4}\def\Nodee{##5}\def\Nodef{##6}}% \next[#6]% \def\next[##1`##2`##3`##4`##5`##6`##7]{% \def\Labela{##1}\def\Labelb{##2}\def\Labelc{##3}\def\Labeld{##4}% \def\Labele{##5}\def\Labelf{##6}\def\Labelg{##7}}% \next[#7]% \dohSquares/#4/}% \def\dohSquares/#1`#2`#3`#4`#5`#6`#7/{% \Squarepppp(\Xpos,\Ypos)|\Xa\Xc\Xd\Xf|/#1`#3`#4`#6/<\deltaY>% [\Nodea`\Nodeb`\Noded`\Nodee;\Labela`\Labelc`\Labeld`\Labelf]% \advance \Xpos by \topw \Squarepppp(\Xpos,\Ypos)|\Xb\Xd\Xe\Xg|/#2``#5`#7/<\deltaY>% [\Nodeb`\Nodec`\Nodee`\Nodef;\Labelb``\Labele`\Labelg]% \ignorespaces}% \def\hSquares{\ifnextchar({\hSquaresp}{\hSquaresp(0,0)}}% \def\hSquaresp(#1){\ifnextchar|{\hSquarespp(#1)}{\hSquarespp% (#1)|aalmrbb|}}% \def\hSquarespp(#1)|#2|{\ifnextchar/{\hSquaresppp(#1)|#2|}% {\hSquaresppp(#1)|#2|/>`>`>`>`>`>`>/}}% \def\hSquaresppp(#1)|#2|/#3/{% \ifnextchar<{\hSquarespppp(#1)|#2|/#3/}% {\hSquarespppp(#1)|#2|/#3/<\default>}}% \def\vSquarespppp(#1,#2)|#3|/#4/<#5,#6>[#7;#8]{% \Xpos=#1\Ypos=#2% \def\next|##1##2##3##4##5##6##7|{% \def\Xa{##1}\def\Xb{##2}\def\Xc{##3}\def\Xd{##4}% \def\Xe{##5}\def\Xf{##6}\def\Xg{##7}}% \next|#3|% \deltaY=#5% \deltaY=#6% \def\next[##1`##2`##3`##4`##5`##6]{% \def\Nodea{##1}\def\Nodeb{##2}\def\Nodec{##3}% \def\Noded{##4}\def\Nodee{##5}\def\Nodef{##6}}% \next[#7]% \def\next[##1`##2`##3`##4`##5`##6`##7]{% \def\Labela{##1}\def\Labelb{##2}\def\Labelc{##3}\def\Labeld{##4}% \def\Labele{##5}\def\Labelf{##6}\def\Labelg{##7}}% \next[#8]% \dovSquares/#4/\ignorespaces}% \def\dovSquares/#1`#2`#3`#4`#5`#6`#7/{% \setmorphismwidth{\Nodea}{\Nodeb}{\Labela}{\topw}% \setmorphismwidth{\Nodec}{\Noded}{\Labeld}{\botw}% \ratchet{\topw}{\botw}% \setmorphismwidth{\Nodee}{\Nodef}{\Labelg}{\botw}% \ratchet{\topw}{\botw}% \square(\Xpos,\Ypos)|\Xd\Xe\Xf\Xg|/`#5`#6`#7/<\topw,\deltaX>% [\Nodec`\Noded`\Nodee`\Nodef;`\Labele`\Labelf`\Labelg]% \advance \Ypos by \deltaX% \square(\Xpos,\Ypos)|\Xa\Xb\Xc\Xd|/#1`#2`#3`#4/<\topw,\deltaY>% [\Nodea`\Nodeb`\Nodec`\Noded;\Labela`\Labelb`\Labelc`\Labeld]% }% \def\vSquares{\ifnextchar({\vSquaresp}{\vSquaresp(0,0)}}% \def\vSquaresp(#1){\ifnextchar|{\vSquarespp(#1)}{\vSquarespp% (#1)|alrmlrb|}}% \def\vSquarespp(#1)|#2|{\ifnextchar/{\vSquaresppp(#1)|#2|}% {\vSquaresppp(#1)|#2|/>`>`>`>`>`>`>/}}% \def\vSquaresppp(#1)|#2|/#3/{% \ifnextchar<{\vSquarespppp(#1)|#2|/#3/}% {\vSquarespppp(#1)|#2|/#3/<\default>}}% \def\osquarepppp(#1)|#2|/#3`#4`#5`#6/<#7>[#8]{\squarepppp% (#1)|#2|/#3`#4`#5`#6/<#7>[#8]% \let\Nodea\nodea\let\Nodeb\nodeb% \let\Nodec\nodec\let\Noded\noded\Xpos=\xpos\Ypos=\ypos% \deltaX=\deltax \deltaY=\deltay \isquare} \def\cube{\ifnextchar({\osquarep}{\osquarep(0,0)}}% \def\osquarep(#1){\ifnextchar|{\osquarepp(#1)}{\osquarepp(#1)|alrb|}}% \def\osquarepp(#1)|#2|{\ifnextchar/{\osquareppp(#1)|#2|}% {\osquareppp(#1)|#2|/>`>`>`>/}}% \def\osquareppp(#1)|#2|/#3`#4`#5`#6/{% \ifnextchar<{\osquarepppp(#1)|#2|/#3`#4`#5`#6/}% {\osquarepppp(#1)|#2|/#3`#4`#5`#6/<1500,1500>}}% \def\isquarepppp(#1)|#2|/#3`#4`#5`#6/<#7>[#8]{% \squarepppp(#1)|#2|/#3`#4`#5`#6/<#7>[#8]% \ifnextchar|{\cubep}{\cubep|mmmm|}}% \def\cubep|#1|{\ifnextchar/{\cubepp|#1|}{\cubepp|#1|/>`>`>`>/}}% \def\isquare{\ifnextchar({\isquarep}{\isquarep(\default,\default)}}% \def\isquarep(#1){\ifnextchar|{\isquarepp(#1)}{\isquarepp(#1)|alrb|}} \def\isquarepp(#1)|#2|{\ifnextchar/{\isquareppp(#1)|#2|}% {\isquareppp(#1)|#2|/>`>`>`>/}}% \def\isquareppp(#1)|#2|/#3`#4`#5`#6/{% \ifnextchar<{\isquarepppp(#1)|#2|/#3`#4`#5`#6/}% {\isquarepppp(#1)|#2|/#3`#4`#5`#6/<500,500>}}% \def\cubepp|#1#2#3#4|/#5`#6`#7`#8/[#9]{% \def\next[##1`##2`##3`##4]{\gdef\Labela{##1}% \gdef\Labelb{##2}\gdef\Labelc{##3}\gdef\Labeld{##4}}\next[#9]% \xend\xpos \yend\ypos \Xend\xend\advance\Xend by -\Xpos \Yend\yend\advance\Yend by -\Ypos \domorphism(\Xpos,\Ypos)|#2|/#6/<\Xend,\Yend>[\Nodeb`\nodeb;\Labelb]% \advance\Xpos by-\deltaX \advance\xend by-\deltax \Xend\xend\advance\Xend by -\Xpos \domorphism(\Xpos,\Ypos)|#1|/#5/<\Xend,\Yend>[\Nodea`\nodea;\Labela]% \advance\Ypos by-\deltaY \advance\yend by-\deltay \Yend\yend\advance\Yend by -\Ypos \domorphism(\Xpos,\Ypos)|#3|/#7/<\Xend,\Yend>[\Nodec`\nodec;\Labelc]% \advance\Xpos by\deltaX \advance\xend by\deltax \Xend\xend\advance\Xend by -\Xpos \domorphism(\Xpos,\Ypos)|#4|/#8/<\Xend,\Yend>[\Noded`\noded;\Labeld]% \ignorespaces} \def\setwdth#1#2{\setbox0\hbox{$#1$}\wdth=\wd0 \setbox0\hbox{$#2$}\ifnum\wdth<\wd0 \wdth=\wd0 \fi} \def\tx^#1_#2{\allowbreak\edef\next{#1}\edef\nextt{#2} \setwdth{#1}{#2}\deltax=\wdth \divide \deltax by \ul \advance \deltax by 100 \ratchet{\deltax}{200} \ifx\next\empty \ifx\nextt\empty \>\xy \ar(\deltax,0)\endxy\>% \else \>\xy \ar_{#2}(\deltax,0)\endxy\>% \fi \else \ifx\nextt\empty \>\xy \ar^{#1}(\deltax,0)\endxy\>% \else \>\xy \ar^{#1}_{#2}(\deltax,0)\endxy\>% \fi \fi} \def\txx^#1{\ifnextchar_{\tx^{#1}}{\tx^{#1}_{}}} \def\to{\ifnextchar^{\txx}{\txx^{}}} \def\txleft^#1_#2{\allowbreak\edef\next{#1}\edef\nextt{#2} \setwdth{#1}{#2}\deltax=\wdth \divide \deltax by \ul \advance \deltax by 100 \ratchet{\deltax}{200} \ifx\next\empty \ifx\nextt\empty \>\xy \ar@{<-}(\deltax,0)\endxy\>% \else \>\xy \ar@{<-}_{#2}(\deltax,0)\endxy\>% \fi \else \ifx\nextt\empty \>\xy \ar@{<-}^{#1}(\deltax,0)\endxy\>% \else \>\xy \ar@{<-}^{#1}_{#2}(\deltax,0)\endxy\>% \fi \fi} \def\txxleft^#1{\ifnextchar_{\txleft^{#1}}{\txleft^{#1}_{}}} \def\toleft{\ifnextchar^{\txxleft}{\txxleft^{}}} \def\monx^#1_#2{\allowbreak\edef\next{#1}\edef\nextt{#2} \setwdth{#1}{#2}\deltax=\wdth \divide \deltax by \ul \advance \deltax by 125 \ratchet{\deltax}{225} \ifx\next\empty \ifx\nextt\empty \>\xy \ar@{ >->}(\deltax,0)\endxy\>% \else \>\xy \ar@{ >->}_{#2}(\deltax,0)\endxy\>% \fi \else \ifx\nextt\empty \>\xy \ar@{ >->}^{#1}(\deltax,0)\endxy\>% \else \>\xy \ar@{ >->}^{#1}_{#2}(\deltax,0)\endxy\>% \fi \fi} \def\monxx^#1{\ifnextchar_{\monx^{#1}}{\monx^{#1}_{}}} \def\mon{\ifnextchar^{\monxx}{\monxx^{}}} \def\monleftx^#1_#2{\allowbreak\edef\next{#1}\edef\nextt{#2} \setwdth{#1}{#2}\deltax=\wdth \divide \deltax by \ul \advance \deltax by 125 \ratchet{\deltax}{225} \ifx\next\empty \ifx\nextt\empty \>\xy \ar@{<-< }(\deltax,0)\endxy\>% \else \>\xy \ar@{<-< }_{#2}(\deltax,0)\endxy\>% \fi \else \ifx\nextt\empty \>\xy \ar@{<-< }^{#1}(\deltax,0)\endxy\>% \else \>\xy \ar@{<-< }^{#1}_{#2}(\deltax,0)\endxy\>% \fi \fi} \def\monleftxx^#1{\ifnextchar_{\monleftx^{#1}}{\monleftx^{#1}_{}}} \def\monleft{\ifnextchar^{\monleftxx}{\monleftxx^{}}} \def\\epileftx^#1_#2{\allowbreak\edef\next{#1}\edef\nextt{#2} \setwdth{#1}{#2}\deltax=\wdth \divide \deltax by \ul \advance \deltax by 125 \ratchet{\deltax}{225} \ifx\next\empty \ifx\nextt\empty \>\xy \ar@{<<-}(\deltax,0)\endxy\>% \else \>\xy \ar@{<<-}_{#2}(\deltax,0)\endxy\>% \fi \else \ifx\nextt\empty \>\xy \ar@{<<-}^{#1}(\deltax,0)\endxy\>% \else \>\xy \ar@{<<-}^{#1}_{#2}(\deltax,0)\endxy\>% \fi \fi} \def\\epileftxx^#1{\ifnextchar_{\\epileftx^{#1}}{\\epileftx^{#1}_{}}} \def\\epileft{\ifnextchar^{\\epileftxx}{\\epileftxx^{}}} \def\epix^#1_#2{\allowbreak\edef\next{#1}\edef\nextt{#2} \setwdth{#1}{#2}\deltax=\wdth \divide \deltax by \ul \advance \deltax by 125 \ratchet{\deltax}{225} \ifx\next\empty \ifx\nextt\empty \>\xy \ar@{->>}(\deltax,0)\endxy\>% \else \>\xy \ar@{->>}_{#2}(\deltax,0)\endxy\>% \fi \else \ifx\nextt\empty \>\xy \ar@{->>}^{#1}(\deltax,0)\endxy\>% \else \>\xy \ar@{->>}^{#1}_{#2}(\deltax,0)\endxy\>% \fi \fi} \def\epixx^#1{\ifnextchar_{\epix^{#1}}{\epix^{#1}_{}}} \def\epi{\ifnextchar^{\epixx}{\epixx^{}}} \def\twx^#1_#2{\allowbreak\edef\next{#1}\edef\nextt{#2} \setwdth{#1}{#2}\deltax=\wdth \divide \deltax by \ul \advance \deltax by 100 \ratchet{\deltax}{200} \ifx\next\empty \ifx\nextt\empty \>\xy \ar@<2.5pt>(\deltax,0) \ar@<-2.5pt>(\deltax,0) \endxy\>% \else \>\xy \ar@<2.5pt>(\deltax,0) \ar@<-2.5pt>_{#2}(\deltax,0) \endxy\>% \fi \else \ifx\nextt\empty \>\xy \ar@<2.5pt>^{#1}(\deltax,0) \ar@<-2.5pt>(\deltax,0) \endxy\>% \else \>\xy \ar@<2.5pt>^{#1}(\deltax,0) \ar@<-2.5pt>_{#2}(\deltax,0) \endxy\>% \fi \fi} \def\twxx^#1{\ifnextchar_{\twx^{#1}}{\twx^{#1}_{}}} \def\two{\ifnextchar^{\twxx}{\twxx^{}}} \def\twleftx^#1_#2{\allowbreak\edef\next{#1}\edef\nextt{#2} \setwdth{#1}{#2}\deltax=\wdth \divide \deltax by \ul \advance \deltax by 100 \ratchet{\deltax}{200} \ifx\next\empty \ifx\nextt\empty \>\xy \ar@{<-}@<2.5pt>(\deltax,0) \ar@{<-}@<-2.5pt>(\deltax,0) \endxy\>% \else \>\xy \ar@{<-}@<2.5pt>(\deltax,0) \ar@{<-}@<-2.5pt>_{#2}(\deltax,0) \endxy\>% \fi \else \ifx\nextt\empty \>\xy \ar@{<-}@<2.5pt>^{#1}(\deltax,0) \ar@{<-}@<-2.5pt>(\deltax,0) \endxy\>% \else \>\xy \ar@{<-}@<2.5pt>^{#1}(\deltax,0) \ar@{<-}@<-2.5pt>_{#2}(\deltax,0) \endxy\>% \fi \fi} \def\twleftxx^#1{\ifnextchar_{\twleftx^{#1}}{\twleftx^{#1}_{}}} \def\twoleft{\ifnextchar^{\twleftxx}{\twleftxx^{}}} \def\twoar(#1,#2){{% \scalefactor{0.1} \deltax#1\deltay#2% \deltaX=\ifnum\deltax<0-\fi\deltax \deltaY=\ifnum\deltay<0-\fi\deltay \Xend\deltax \multiply \Xend by \deltax \Yend\deltay \multiply \Yend by \deltay \advance\Xend by \Yend \multiply \Xend by 3 % Xend = 3*(\deltax^2 + \deltay^2) \ifnum \deltaX > \deltaY \multiply \deltaX by 3 \advance \deltaX by \deltaY \else \multiply \deltaY by 3 \advance \deltaX by \deltaY \fi % \deltaX = 3*max(|\deltax|,|\deltay|) + min(|\deltax|,|\deltay|) % a good approximation to sqrt(\deltax^2 + \deltay^2). \multiply\deltax by 500 \multiply\deltay by 500 \xpos\deltax \multiply \xpos by 3 \divide\xpos by \deltaX % \xpos = (1500*\deltax)/\deltaX \Xpos\deltax \multiply \Xpos by \deltaX \divide \Xpos by \Xend % \Xpos = (\500*\deltax*\deltaX)/Xend \advance \xpos by \Xpos % \xpos = (1500*\deltax)/\deltaX + (\500*\deltax*\deltaX)/Xend \ypos\deltay \multiply \ypos by 3 \divide\ypos by \deltaX % \ypos = (1500*\deltay)/\deltaX \Ypos\deltay \multiply \Ypos by \deltaX \divide \Ypos by \Xend % \Xpos = (\500*\deltay*\deltaX)/Xend \advance \ypos by \Ypos % \ypos = (1500*\deltay)/\deltaX + (\500*\deltay*\deltaX)/Xend \xy \ar@{=>}(\xpos,\ypos) \endxy }} \def\iiixiiipppppp(#1,#2)|#3|/#4/<#5>#6<#7>[#8;#9]{% \xpos#1\ypos#2\relax \def\next|##1##2##3##4##5##6##7|{\def\xa{##1}\def\xb{##2}% \def\xc{##3}\def\xd{##4}\def\xe{##5}\def\xf{##6}\nextt|##7|}% \def\nextt|##1##2##3##4##5##6|{\def\xg{##1}\def\xh{##2}% \def\xi{##3}\def\xj{##4}\def\xk{##5}\def\xl{##6}}% \next|#3|% \def\next<##1,##2>{\deltax##1\deltay##2}% \next<#5>% \def\next<##1,##2>{\deltaX##1\deltaY##2}% \next<#7> \def\next##1{\topw##1 \ifodd\topw \def\zl{}\else\def\zl{\relax}\fi \divide\topw by 2 \ifodd\topw \def\zk{}\else\def\zk{\relax}\fi \divide\topw by 2 \ifodd\topw \def\zj{}\else\def\zj{\relax}\fi \divide\topw by 2 \ifodd\topw \def\zi{}\else\def\zi{\relax}\fi \divide\topw by 2 \ifodd\topw \def\zh{}\else\def\zh{\relax}\fi \divide\topw by 2 \ifodd\topw \def\zg{}\else\def\zg{\relax}\fi \divide\topw by 2 \ifodd\topw \def\zf{}\else\def\zf{\relax}\fi \divide\topw by 2 \ifodd\topw \def\ze{}\else\def\ze{\relax}\fi \divide\topw by 2 \ifodd\topw \def\zd{}\else\def\zd{\relax}\fi \divide\topw by 2 \ifodd\topw \def\zc{}\else\def\zc{\relax}\fi \divide\topw by 2 \ifodd\topw \def\zb{}\else\def\zb{\relax}\fi \divide\topw by 2 \ifodd\topw \def\za{}\else\def\za{\relax}\fi}% \next{#6}% \def\next[##1`##2`##3`##4`##5`##6`##7`##8`##9]{% \def\nodea{##1}\def\nodeb{##2}\def\nodec{##3}% \def\noded{##4}\def\nodee{##5}\def\nodef{##6}% \def\nodeg{##7}\def\nodeh{##8}\def\nodei{##9}}% \next[#8]% \def\next[##1`##2`##3`##4`##5`##6`##7]{% \def\labela{##1}\def\labelb{##2}\def\labelc{##3}% \def\labeld{##4}\def\labele{##5}\def\labelf{##6}\nextt[##7]}% \def\nextt[##1`##2`##3`##4`##5`##6]{% \def\labelg{##1}\def\labelh{##2}\def\labeli{##3}% \def\labelj{##4}\def\labelk{##5}\def\labell{##6}}% \next[#9]% \def\next/##1`##2`##3`##4`##5`##6`##7/{% \morphism(\xpos,\ypos)|\xe|/##5/<\deltax,0>[\nodeg`\nodeh;\labele]% \ifx\zi\empty \morphism(\xpos,\ypos)||/<-/<-\deltaX,0>[\nodeg`0;]\fi \ifx\zd\empty \morphism(\xpos,\ypos)||<0,-\deltaY>[\nodeg`0;]\fi \advance\xpos by \deltax \morphism(\xpos,\ypos)|\xf|/##6/<\deltax,0>[\nodeh`\nodei;\labelf]% \ifx\ze\empty \morphism(\xpos,\ypos)||<0,-\deltaY>[\nodeh`0;]\fi \advance\xpos by \deltax \ifx\zf\empty \morphism(\xpos,\ypos)||<0,-\deltaY>[\nodei`0;]\fi \ifx\zl\empty \morphism(\xpos,\ypos)||<\deltaX,0>[\nodei`0;]\fi \advance\ypos by \deltay \ifx\zk\empty \morphism(\xpos,\ypos)||<\deltaX,0>[\nodef`0;]\fi \advance\xpos by -\deltax \morphism(\xpos,\ypos)|\xd|/##4/<\deltax,0>[\nodee`\nodef;\labeld]% \advance\xpos by -\deltax \morphism(\xpos,\ypos)|\xc|/##3/<\deltax,0>[\noded`\nodee;\labelc]% \ifx\zh\empty \morphism(\xpos,\ypos)||/<-/<-\deltaX,0>[\noded`0;]\fi \advance\ypos by \deltay \morphism(\xpos,\ypos)|\xa|/##1/<\deltax,0>[\nodea`\nodeb;\labela]% \ifx\zg\empty \morphism(\xpos,\ypos)||/<-/<-\deltaX,0>[\nodea`0;]\fi \ifx\za\empty \morphism(\xpos,\ypos)||/<-/<0,\deltaY>[\nodea`0;]\fi \advance\xpos by \deltax \morphism(\xpos,\ypos)|\xb|/##2/<\deltax,0>[\nodeb`\nodec;\labelb]% \ifx\zb\empty \morphism(\xpos,\ypos)||/<-/<0,\deltaY>[\nodeb`0;]\fi \advance\xpos by \deltax \ifx\zc\empty \morphism(\xpos,\ypos)||/<-/<0,\deltaY>[\nodec`0;]\fi \ifx\zj\empty \morphism(\xpos,\ypos)||<\deltaX,0>[\nodec`0;]\fi \nextt/##7/} \def\nextt/##1`##2`##3`##4`##5`##6/{% \morphism(\xpos,\ypos)|\xi|/##3/<0,-\deltay>[\nodec`\nodef;\labeli]% \advance\xpos by -\deltax \morphism(\xpos,\ypos)|\xh|/##2/<0,-\deltay>[\nodeb`\nodee;\labelh]% \advance\xpos by -\deltax \morphism(\xpos,\ypos)|\xg|/##1/<0,-\deltay>[\nodea`\noded;\labelg]% \advance\ypos by -\deltay \morphism(\xpos,\ypos)|\xj|/##4/<0,-\deltay>[\noded`\nodeg;\labelj]% \advance\xpos by \deltax \morphism(\xpos,\ypos)|\xk|/##5/<0,-\deltay>[\nodee`\nodeh;\labelk]% \advance\xpos by \deltax \morphism(\xpos,\ypos)|\xl|/##6/<0,-\deltay>[\nodef`\nodei;\labell]}% \next/#4/} \def\iiixiii{\ifnextchar({\iiixiiip}{\iiixiiip(0,0)}}% \def\iiixiiip(#1){\ifnextchar|{\iiixiiipp(#1)}% {\iiixiiipp(#1)|aammbblmrlmr|}}% \def\iiixiiipp(#1)|#2|{\ifnextchar/{\iiixiiippp(#1)|#2|}% {\iiixiiippp(#1)|#2|/>`>`>`>`>`>`>`>`>`>`>`>/}}% \def\iiixiiippp(#1)|#2|/#3/{% \ifnextchar<{\iiixiiipppp(#1)|#2|/#3/}% {\iiixiiipppp(#1)|#2|/#3/<\default,\default>}}% \def\iiixiiipppp(#1)|#2|/#3/<#4>{\ifnextchar[{\iiixiiippppp(#1)|#2|/#3/% <#4>0<0,0>}{\iiixiiippppp(#1)|#2|/#3/<#4>}}% \def\iiixiiippppp(#1)|#2|/#3/<#4>#5{\ifnextchar<% {\iiixiiipppppp(#1)|#2|/#3/<#4>{#5}}% {\iiixiiipppppp(#1)|#2|/#3/<#4>{#5}<400,400>}}% \catcode`\@=\atcode% From rrosebru@mta.ca Wed May 2 13:46:14 2001 -0300 Return-Path: Received: (from Majordom@localhost) by mailserv.mta.ca (8.11.1/8.11.1) id f42Fwsu13427 for categories-list; Wed, 2 May 2001 12:58:54 -0300 (ADT) X-Authentication-Warning: mailserv.mta.ca: Majordom set sender to cat-dist@mta.ca using -f X-Authentication-Warning: triples.math.mcgill.ca: barr owned process doing -bs Date: Wed, 2 May 2001 06:37:08 -0400 (EDT) From: Michael Barr X-Sender: barr@triples.math.mcgill.ca To: Categories list Subject: categories: diaxydoc.tex Message-ID: MIME-Version: 1.0 Content-Type: TEXT/PLAIN; charset=US-ASCII Sender: cat-dist@mta.ca Precedence: bulk Status: O X-Status: X-Keywords: X-UID: 7 Note: This is not the version that will be posted, but rather for those who have seen earlier versions. But the examples are all the same. \documentclass{article} \input diagxy \xyoption{curve} \textwidth 6in \oddsidemargin 0pt \begin{document} \def\xypic{\hbox{\rm\Xy-pic}} \title{A new diagram package (Version 3)} \author{Michael Barr\\Dept of Math and Stats\\McGill University\\805 Sherbrooke St. W\\Montreal, QC Canada H3A 2K6\\[5pt] barr@barrs.org} \maketitle \section*{Why a new diagram package?} This started when a user of my old package, diagram, wrote to ask me if dashed lines were possible. The old package had dashed lines for horizontal and vertical arrows, but not any other direction. The reason for this was that \LaTeX\ used rules for horizontal and vertical arrows, but had its own fonts for other directions. While rules could be made any size, the smallest lines in other directions were too long for decent looking dashes. Presumably, Lamport was worried about compile time and file size if the lines were too short, considerations that have diminished over the years since. Also arrows could be drawn in only 48 different directions, which is limiting. My macros were not very well implemented for slopes like 4 and 1/4, since I never used such lines. There was certainly an alternative, \xypic, for those who wanted something better. But it was hard to learn and I was not entirely happy with the results. The basic interface used an \verb+\halign+. This meant that no extra space was allotted to an arrow that had a large label. In addition, the different slots could have different horizontal size, which could result in a misshapen diagram. I used it in a paper that had a `W' shaped diagram whose nodes had different widths and the result was quite obviously misshapen. On the other hand, the graphics engine underlying \xypic\ is really quite remarkable and it occurred to me that I could try to redraft diagram as a front end. The result is the current package. It has been tested only with version 3.7, so there is no guarantee it would work with any earlier version (or, for that matter, later). The syntax described below is not compatible with the original diagram package. Every front end of this sort represents a trade-off between simplicity and utility. A package that simply upgraded the syntax to allow more dashed (and dotted) lines would have been just as easy to implement, but would have made poor use of the wonderful possibilities of the underlying \xypic\ package. Also there would have been too many different arrow specifications (they would have had to go at least in the range $[-9,9]$) for easy memory) and still would not have included things like inclusion arrows. To those who would have liked a simpler syntax, I apologize. To those who would want more flexibility, I remind that the entire \xypic\ package is there for use. \subsection*{Errant spaces} There is one point that cannot be made too strongly. {\em Watch for errant spaces.} Unlike the old diagram package, which was carried out in math mode so that spaces were ignored, \xypic\ is not in math mode and spaces will mess up your diagrams. On the other hand, it will not be necessary to enclose duplicate nodes inside \verb+\phantom+, since the registration between different nodes is perfect. In the old package, for reasons that I now understand, objects did not always register properly. This was a flaw built in to the very heart of the package and is not worth correcting, although it could have been done better in the first place. If you see an object in double vision, then the almost certain cause is that a space has gotten in there somewhere. I have attempted to prevent this by liberal use of \verb+\ignorespaces+ in the definitions, but one cannot always be sure and while testing, I found a number seemingly innocuous spaces that messed up diagrams. When in doubt, always terminate a specification with a \verb+%+. See the examples. \subsection*{What's new in version 2} \begin{enumerate} \item \verb+\scalefactor{decimal number}+ changes all dimensions by the factor. \item New macros \verb+\Square, \hSquares, \vSquares+ that calculate their own widths. \item New macro \verb+\cube+. \item Internal macro \verb+\label+ that conflicted with \LaTeX\ renamed. \item Added certain procedures designed for inline and displayed equations that are not full-fledged diagrams. These also calculate the length of the arrow to contain the label. \item Corrected certain spacing anomolies. \item Now does work with plain \TeX. \end{enumerate} \subsection*{What's new in version 3} \begin{enumerate} \item {\bf Two syntax changes:} The \verb+\morphism+ macro now uses the syntax \verb.\morphism[N`N;L]. for consistency with all the shapes. And the back ticks (\verb.`.) has been eliminated from the label placement parameters. It was useless and slightly annoying. Each one consists of exactly one character and the standard \TeX\ parser deals with that automatically. I gave a thought to doing the same for the arrow shape but then anything beyond a single character would require braces, which are also annoying. \item The macro \verb+\square+ has been given defaults and the leading groups of parameters are now optional. The defaults are \verb+(0,0)|a|/>/<500,0>+. The meaning of \verb+a+ on a vertical arrow is to the left if it points up and to the right if it points down. \item The 10\% (actually it was more like 12\%) error in the lengths of 2-arrows at different slopes has been reduced to well under 1\% by using one Newton's method iteration on the original approximation of the square root of \verb-dx^2 + dy^2-. \item The example of a pair of inline arrows had the diagram appearing about 3 points below the line of the text. By enclosing it in a math emvironment, this has been repaired (although the reason mystifies me). \item A very obscure bug in the handling of the \verb+~+ (caused by its being an active character) has been repaired so that you can get a wavy arrow with \verb+~>+ as the arrow shape specification. \end{enumerate} The first one is relatively minor; the second is unlikely to matter since \verb+\to+ and its relatives is much more flexible; the third would arise only if you used wavy arrows. The package seems to have converged. I am not planning on adding any more procedures, although I will try to fix any further bugs that are called to my attention. Thus this version is the one that will be released shortly. \section*{The basic syntax} The basic syntax is built around an operation \verb+\morphism+ that is used as \begin{verbatim} \morphism(x,y)|placement|/{shape}/[N`N;L] \end{verbatim} The last group of parameters is required. They are the source and target nodes of the arrow and the label. The remaining parameters are optional and default to commonly used values. Currently, the \verb+L+ is set in \verb+\scriptstyle+ size, but this can easily be changed by putting \verb+\let\labelstyle=\textstyle+ in your file. The parameters \verb+x+ and \verb+y+ give the location of the source node within a fixed local coordinate system and \verb-x+dx- and \verb-y+dy- and locate the target. To be precise, the first coordinate is the horizontal center of the node and the second is that of the base line. These distances are given in terms of \verb+\ul+'s, (for unitlength), which is user assignable, but currectly is .01em. The parameter \verb+placement+ is one of \verb+a,b,l,r,m+ that stand for above, below, left, right, or mid and describe the positioning of the arrow label on the arrow. If it is given any value other than those five, it is ignored. We describe below why you might want to do this. The label \verb+m+ stands for a label positioned in the middle of a split arrow. When used on a non-vertical arrow, \verb+a+ positions the label above the arrow and \verb+b+ positions it below. On a vertical arrow, the positioning depends on whether the arrow points up or down. Similarly, when used on a non-horizontal arrow, \verb+l+ positions the label to the left and \verb+r+ positions it to the right, while on a horizontal arrow it depends on which way it points. The \verb+shape+ describes the shape of the arrow. An arrow is thought of as consisting of three parts, the tail, the shaft and the head. You may specify just the head, in which case the shaft will be an ordinary line, or all three. However, since the tail can be (and usually is) empty, in practice you can also describe the shaft and tail. In addition, it is possible to modify the arrow in various ways. Although the parameter is shown within braces, the braces can be omitted unless one of the modifier characters is \verb+/+, in which case, {\em the entire parameter} must be put in braces. It is important to note that it will not work just to put the \verb+/+ inside the braces, since this will interfere with the internal parsing of \xypic. The head and tail shapes are basically one of \verb+>+, \verb+>>+, \verb+(+, \verb+)+, \verb*+ >+, and \verb*+< +. Each of these may also be preceded by \verb+^+ or \verb+_+ and others are user definable. For details, see the \xypic\ reference manual. The first of these is an ordinary head, while the second is for an epic arrow. The third is not much used, but the superscripted version makes and inclusion tail, as will be illustrated below. The reverse ones give reversed arrowheads. The sign \verb*+ + stands for an obligatory space and it leaves extra space for a tailed (monic) arrow, which otherwise runs into the source node. Although there are many possibilities for shafts, including alphanumeric characters, there are basically three that interest us: \verb+-+, which is an ordinary shaft, \verb+--+, which produces a dashed arrow, \verb+=+, which gives a double arrow (although with only one arrowhead), and \verb+.+, which makes a dotted arrow. Thus \verb+>+ or \verb+->+ will produce an ordinary arrow, \verb+->>+ an epic arrow, \verb*+ >->+ makes a monic arrow, and \verb+-->>+ would make a dashed epic arrow. The descriptions \verb+<-, <<-,+ \verb*+<-< +, and \verb+<<--+ give the reversed versions. Note that \verb+<+ does not give a reversed arrow, since \xypic\ interprets that as a reversed head, not a tail. If the shape parameter begins with an \verb+@+, it is interpreted differently. In that case, it has the form \verb+@{shape}@+ modifier, where the modifier is as described in the \xypic\ reference guide. I just mention a couple of them. The parameter \verb+@{->}@<3pt>+, for example, would give an ordinary arrow moved three points in the direction perpendicular to that of the arrow. If you give \verb+{@{-->}@/^5pt/}+, you will get an epic arrow that is curved in the direction perpendicular to the direction of the arrow by five points. (As far as I can tell, there is no difference between \verb+^-5pt+ and \verb+_5pt+ so the syntax could be simplified and made consistent with that of \verb++ described above.) It is imperative that a specification such as \verb+@{>}@/5pt/+ be enclosed in braces because of the \verb+/+s. \subsection*{A word about parameters} I have already mentioned the necessity of enclosing certain arrow shape specifications in braces. Because of the way \TeX\ operates, I have used a number of different delimiters: \verb+(, ), |, /, [, ], `, ;+. Any of these that appear inside an argument could conceivably cause problems. They were chosen as the least likely to appear inside mathematics (except for \verb+(,)+ which appear in positions that are unlikely to cause problems). However, be warned that this is a possible cause of mysterious error messages. If this happens, enclosing the offending parameter in braces should cure the problem. The exceptions come when the braces interfere with \xypic's somewhat arcane parsing mechanism. One place I have found it imperative to use braces is if you attempt to use a disk as a tip. According to the \xypic\ documentation, the tip * will give you a disk as an arrowhead. However, as I have discovered by experiment, the first three of \begin{verbatim} \morphism(0,300)|a|/-*/<500,0>[A`B;f] \morphism(0,0)|a|/{-*}/<500,0>[A`B;f] \morphism(0,0)|a|/{*}/<500,0>[A`B;f] \morphism(0,0)|a|/-{*}/<500,0>[A`B;f] \end{verbatim} give only an error message. Only the fourth works: $$\bfig \morphism(0,0)|a|/-{*}/<500,0>[A`B;f] \efig$$ This seems to be a feature of \xypic's parsing mechanism. In addition to the diagrams, there are macros that are intended to be used inline to make horizontal arrows, pointing left or right, plain, monic, epic, or user-definable shapes, and calculating their own length to fit the label. Finally, there is a macro for making short 2-arrows that may be placed (actually, \verb+\place+d) anywhere in a diagram. \section*{Shapes} Using the basic \verb+\morphism+ macro, I have a defined a number of shapes, squares (really rectangles) and variously oriented triangles and a few compound shapes. The basic shapes are exactly the same as in the old diagram package, but the options are done entirely differently. Here is the syntax of the \verb+\square+ macro: \begin{verbatim} \square(x,y)|pppp|/{sh}`{sh}`{sh}`{sh}/[N`N`N`N;L`L`L`L] \end{verbatim} Each of the first four sets of parameters is optional and any subset of them can be omitted. (Note that only the sets can be omitted, once you give \verb+dx+, you also have to give \verb+dy+ and so on.) The first two describe the horizontal and vertical dimensions of the lower left corner of the square, the next four give the label placements using the same five characters previously described. The next four give the shapes of the arrows using the same syntax as discussed above. The last group is horizontal and vertical size of the square. More precisely, the \verb+x+ coordinate is that of the midpoint of the node, while the \verb+y+ coordinate is that of the baseline of the node. This is entirely based on \xypic. In the case of other shapes, discussed below, the positioning parameter may be a bit different. The \verb+x+ coordinate is the midpoint of the leftmost node and the \verb+y+ coordinate is the baseline of the lowest node. In the case of the \verb+\qtriangle+, \verb+\Vtriangle+, and \verb+\Ctriangle+ described below, these are different nodes. What this positioning means is that if you specify the coordinates and sizes correctly the shapes will automatically fit together. The last example on Page~\pageref{TTTdiag} illustrates this. Here is a listing of the shapes, together with the groups of parameters. In all cases, the first four groups are optional and any subset of them will work. However, they must come in the order given. Note that the names of the triangles are related to the shape as the shape that best approximates the shape of the letter. For example, a \verb+\ptriangle+ is a right triangle that has its hypotenuse going from upper right to lower left. Triangles with lower case names have their legs horizontal and vertical and the dimension parameters are the lengths of the legs. Those with capitalized names have their hypotenuse horizontal or vertical. In those cases, one of \verb+dx+ or \verb+dy+ is the length of a leg and the other is {\em half} the length of the hypotenuse. In all cases, the order of the nodes and of the arrows is linguistic, first moving from left to right and then down. The defaults are reasonable, but with triangles, there is not always a natural direction for arrows. I always made mistakes in the order with my macros and this is certainly a defect. But the order is the same. In every case the braces around the shape specification can be removed unless it includes the following delimiter (that is, \verb+`+ or \verb+/+, as the case may be.) \begin{verbatim} \square(x,y)|pppp|/{sh}`{sh}`{sh}`{sh}/% [N`N`N`N;L`L`L`L] \ptriangle(x,y)|ppp|/{sh}`{sh}`{sh}/[N`N`N;L`L`L] \qtriangle(x,y)|ppp|/{sh}`{sh}`{sh}/[N`N`N;L`L`L] \dtriangle(x,y)|ppp|/{sh}`{sh}`{sh}/[N`N`N;L`L`L] \btriangle(x,y)|ppp|/{sh}`{sh}`{sh}/[N`N`N;L`L`L] \Atriangle(x,y)|ppp|/{sh}`{sh}`{sh}/[N`N`N;L`L`L] \Vtriangle(x,y)|ppp|/{sh}`{sh}`{sh}/[N`N`N;L`L`L] \Ctriangle(x,y)|ppp|/{sh}`{sh}`{sh}/[N`N`N;L`L`L] \Dtriangle(x,y)|ppp|/{sh}`{sh}`{sh}/[N`N`N;L`L`L] \Atrianglepair(x,y)|ppppp|/{sh}`{sh}`{sh}`{sh}`{sh}/% [N`N`N`N;L`L`L`L`L] \Vtrianglepair(x,y)|ppppp|/{sh}`{sh}`{sh}`{sh}`{sh}/% [N`N`N`N;L`L`L`L`L] \Ctrianglepair(x,y)|ppppp|/{sh}`{sh}`{sh}`{sh}`{sh}/% [N`N`N`N;L`L`L`L`L] \Dtrianglepair(x,y)|ppppp|/{sh}`{sh}`{sh}`{sh}`{sh}/% [N`N`N`N;L`L`L`L`L] \end{verbatim} Note that the \verb+%+ signs are required if you break the macro at such points. See also the discussion of errant spaces above. To make a diagram, you have to enclose it inside \verb+\xy ... \endxy+. You will almost always want it displayed, for which the simplest is to enclose it in \verb+$$\xy ... \endxy$$+. For old times' sake, I have also let \verb+\bfig+ and \verb+\efig+ be synonyms for \verb+\xy+ and \verb+\endxy+, resp. (In case you wonder, these go all the back to a main frame formatter running at McGill when Charles Wells and I were first writing TTT, where \verb+.BFIG+ and \verb+.EFIG+ were used to make displays, at least as far as that primitive formatter was capable of.) \section{Examples} Many people---including me--- learn mainly by example and I will give a number of examples here. The formal syntax can be learned in the \xypic\ reference manual. We begin with \begin{verbatim} $$\bfig \morphism[A`B;f] \morphism(0,300)[A`B;f] \morphism(0,600)|m|[A`B;f] \morphism(0,900)/<-/[A`B;f] \morphism(900,500)<0,-500>[A`B;f] \morphism(1200,0)<0,500>[A`B;f] \efig$$ \end{verbatim} which gives the diagram $$\bfig \morphism[A`B;f] \morphism(0,300)[A`B;f] \morphism(0,600)|m|[A`B;f] \morphism(0,900)/<-/[A`B;f] \morphism(900,500)<0,-500>[A`B;f] \morphism(1200,0)<0,500>[A`B;f] \efig$$ \begin{verbatim} $$\bfig \square[A`B`C`D;e`f`g`m] \efig$$ \end{verbatim} produces $$\bfig \square[A`B`C`D;e`f`g`m] \efig$$ This can be modified, for example \begin{verbatim} $$\bfig \square/>>`>`>` >->/[A`B`C`D;e`f`g`m] \efig$$ \end{verbatim} produces $$\bfig \square/>>`>`>` >->/[A`B`C`D;e`f`g`m] \efig$$ This can be put together with a morphism as follows: \begin{verbatim} $$\bfig \square/>>`>`>` >->/[A`B`C`D;e`f`g`m] \morphism(500,500)|m|/.>/<-500,-500>[B`C;h] \efig$$ \end{verbatim} which makes a familiar diagram: $$\bfig \square/>>`>`>` >->/[A`B`C`D;e`f`g`m] \morphism(500,500)|m|/.>/<-500,-500>[B`C;h] \efig$$ The same diagram could have been made by \begin{verbatim} $$\bfig \ptriangle|alm|/>>`>`.>/[A`B`C;e`f`h] \dtriangle/`>` >->/[B`C`D;`g`m] \efig$$ \end{verbatim} There are four macros for making pairs of triangles put together: $$\bfig \Vtrianglepair[A`B`C`D;f`g`h`k`l] \efig$$ comes from \begin{verbatim} $$\bfig \Vtrianglepair[A`B`C`D;f`g`h`k`l] \efig$$ \end{verbatim} You can fit two squares together, horizontally: \begin{verbatim} $$\bfig \square|almb|[A`B`C`D;f`g`h`k] \square(500,0)/>``>`>/[B`E`D`F;l``m`n] \efig$$ \end{verbatim} $$\bfig \square|almb|[A`B`C`D;f`g`h`k] \square(500,0)/>``>`>/[B`E`D`F;l``m`n] \efig$$ or vertically \begin{verbatim} $$\bfig \square(0,500)|alrm|[A`B`C`D;f`g`h`k] \square/`>`>`>/[C`D`E`F;`l`m`n] \efig$$ \end{verbatim} $$\bfig \square(0,500)|alrm|[A`B`C`D;f`g`h`k] \square/`>`>`>/[C`D`E`F;`l`m`n] \efig$$ or a square and a triangle \begin{verbatim} $$\bfig \Ctriangle/<-`>`>/<400,400>[\hbox{\rm rec}(A,B)`B`X;r_0(A,B)`f`t_0] \square(400,0)/<-``>`<-/<1000,800>[\hbox{\rm rec}(A,B)`A\times\hbox{\rm rec}(A,B)`X`A\times X;r(A,B)``\hbox{\rm id}_A\times f`t] \efig$$ \end{verbatim} gives the diagram $$\bfig \Ctriangle/<-`>`>/<400,400>[\hbox{\rm rec}(A,B)`B`X;r_0(A,B)`f`t_0] \square(400,0)/<-``>`<-/<1000,800>[\hbox{\rm rec}(A,B)`A\times\hbox{\rm rec}(A,B)`X`A\times X;r(A,B)``\hbox{\rm id}_A\times f`t] \efig$$ This diagram is on page 361 of the third edition of Category Theory for Computing Science to describe recursion. Here is an example using the procedure for sliding an arrow sideways. This one could even be used in a text, $\xy \morphism(0,0)|a|/@{>}@<3pt>/<400,0>[A`B;d] \morphism(0,0)|b|/@{>}@<-3pt>/<400,0>[A`B;e]\endxy$ which was made using \begin{verbatim} $\xy \morphism(0,0)|a|/@{>}@<3pt>/<400,0>[A`B;d] \morphism(0,0)|b|/@{>}@<-3pt>/<400,0>[A`B;e]\endxy$ \end{verbatim} Indidentally, if you don't put this in math mode, the diagram will come out too low, for reasons I do not understand but must be buried within the \xypic\ code. This can be seen in an earlier version of thid document. Later we will introduce a number of inline procedures. Something a bit different that illustrates the use of another shaft \verb+=+ that gives a 2-arrow, as well as curved arrows: \begin{verbatim} $$\bfig \morphism(0,0)|a|/{@{>}@/^1em/}/<500,0>[A`B;f] \morphism(0,0)|b|/{@{>}@/_1em/}/<500,0>[A`B;g] \morphism(250,50)|a|/=>/<0,-100>[``] \efig$$ \end{verbatim} $$\bfig \morphism(0,0)|a|/{@{>}@/^1em/}/<500,0>[A`B;f] \morphism(0,0)|b|/{@{>}@/_1em/}/<500,0>[A`B;g] \morphism(250,50)|a|/=>/<0,-100>[`;] \efig$$ In order to use curved arrows, you must insert \verb+\xyoption{curve}+ into your file. Here are two ways of doing three arrows between two objects, depending on what you like: \begin{verbatim} $$\bfig \morphism(0,0)|a|/@{>}@<5pt>/<500,0>[A`B;f] \morphism(0,0)|m|/@{>}/<500,0>[A`B;g] \morphism(0,0)|b|/@{>}@<-5pt>/<500,0>[A`B;h] \efig$$ \end{verbatim} which gives $$\bfig \morphism(0,0)|a|/@{>}@<5pt>/<500,0>[A`B;f] \morphism(0,0)|m|/@{>}/<500,0>[A`B;g] \morphism(0,0)|b|/@{>}@<-5pt>/<500,0>[A`B;h] \efig$$ and \begin{verbatim} $$\bfig \morphism(0,0)|a|/{@{>}@/^5pt/}/<500,0>[A`B;f] \morphism(0,0)|m|/@{>}/<500,0>[A`B;g] \morphism(0,0)|b|/{@{>}@/^-5pt/}/<500,0>[A`B;h] \efig$$ \end{verbatim} which gives $$\bfig \morphism(0,0)|a|/{@{>}@/^5pt/}/<500,0>[A`B;f] \morphism(0,0)|m|/@{>}/<500,0>[A`B;g] \morphism(0,0)|b|/{@{>}@/^-5pt/}/<500,0>[A`B;h] \efig$$ Either of these could also be used inline. There is a macro \verb+\place(x,y)[N]+ where \verb+N+ is any object that places that object anywhere. I have changed the name in order to avoid clashing with the \LaTeX\ picture mode's \verb+\put+. Here is an example that uses a construction that is undocumented here, but uses a documented \Xy\ construction: \begin{verbatim} \newbox\anglebox \setbox\anglebox=\hbox{\xy \POS(75,0)\ar@{-} (0,0) \ar@{-} (75,75)\endxy} \def\angle{\copy\anglebox} $$\bfig \square[A`B`C`D;f`g`h`k] \place(100,400)[\angle] \efig$$ \end{verbatim} \newbox\anglebox \setbox\anglebox=\hbox{\xy \POS(75,0)\ar@{-} (0,0) \ar@{-} (75,75)\endxy} \def\angle{\copy\anglebox} $$\bfig \square[A`B`C`D;f`g`h`k] \place(100,400)[\angle] \efig$$ Notice that you get a headless arrow by using \verb+\ar@{-}+. Here is a special code installed at the request of Jonathon Funk: \begin{verbatim} $$\bfig \pullback|brrb|<800,800>[P`X`Y`Z;t`u`v`w]% |amb|/>`-->`>/<500,500>[A;f`g`h] \efig$$ \end{verbatim} $$\bfig \pullback|brrb|<800,800>[P`X`Y`Z;t`u`v`w]% |amb|/>`-->`>/<500,500>[A;f`g`h] \efig$$ The full syntax for this is \begin{verbatim} \pullback(x,y)|pppp|/{sh}`{sh}`{sh}`{sh}/[N`N`N`N;L`L`L]% |ppp|/{sh}`{sh}`{sh}/[N;L`L`L] \end{verbatim} Of these only the nodes placed inside brackets are obligatory. The first sets of parameters are exactly as for \verb+\square+ and the remaining parameters are for the nodes and labels of the outer arrows. There is no positioning parameters for them; rather you set the horizontal and vertical separations of the outer node from the square. Here are some more special constructions. In general, if you are doing a square, you should use \verb+\Square+ instead of \verb+\square+ because if figures its own width. The syntax is almost the same, except that \verb+dx+ is omitted. For example, \begin{verbatim} $$\bfig \Square/^{ (}->`>`>`^{ (}->/<350>[{\rm Hom}(A,2^B)`{\rm Sub}(A\times B)` {\rm Hom}(A',2^{B'})`{\rm Sub}(A'\times B');\alpha(A,B)```\alpha(A',B')] \efig$$ \end{verbatim} will produce the square $$\bfig \Square/^{ (}->`>`>`^{ (}->/<350>[{\rm Hom}(A,2^B)`{\rm Sub}(A\times B)` {\rm Hom}(A',2^{B'})`{\rm Sub}(A'\times B');\alpha(A,B)```\alpha(A',B')] \efig$$ There are a couple of points to note here. Note the use of the argument \verb+^{ (}->+ to get the inclusion arrow. The complication is created by the necessity of adding a bit of extra space before the hook. You get pretty much the same effect by putting a bit of extra space after the node: \begin{verbatim} $$\bfig \Square/^(->`>`>`^(->/<350>[{\rm Hom}(A,2^B)\,`{\rm Sub}(A\times B)` {\rm Hom}(A',2^{B'})\,`{\rm Sub}(A'\times B');\alpha(A,B)```\alpha(A',B')] \efig$$ \end{verbatim} The full syntax is \begin{verbatim} \Square(x,y)|pppp|/{sh}`{sh}`{sh}`{sh}/[N`N`N`N;L`L`L`L] \end{verbatim} There are also macros for placing two \verb+\Square+s together horizontally or vertically. The first is \verb+\hSquares+ with the syntax \begin{verbatim} \hSquares(x,y)|ppppppp|/{sh}`{sh}`{sh}`{sh}`{sh}`{sh}`{sh}/% [N`N`N`N`N`N;L`L`L`L`L`L`L] \end{verbatim} The second is \verb+\vSquares+ with a similar syntex except that there are two \verb+dy+ parameters, one for each square: \begin{verbatim} \hSquares(x,y)|ppppppp|/{sh}`{sh}`{sh}`{sh}`{sh}`{sh}`{sh}/% [N`N`N`N`N`N;L`L`L`L`L`L`L] \end{verbatim} Similarly, there are four macros for making pairs of triangles put together. For example, $$\bfig \Vtrianglepair[A`B`C`D;f`g`h`k`l] \efig$$ comes from \begin{verbatim} $$\bfig \Vtrianglepair[A`B`C`D;f`g`h`k`l] \efig$$ \end{verbatim} There is a macro for making cubes. The syntax is \begin{verbatim} \cube(x,y)|pppp|/{sh}`{sh}`{sh}`{sh}/[N`N`N`N;L`L`L`L]% (x,y)|pppp|/{sh}`{sh}`{sh}`{sh}/[N`N`N`N;L`L`L`L]% |pppp|/{sh}`{sh}`{sh}`{sh}/[L`L`L`L] \end{verbatim} The first line of parameters is for the outer square and the second for the inner square, while the remaining parameters are for the arrows between the squares. Only the parameters in square brackets are required; there are defaults for the others. Here is an example: \begin{verbatim} $$\bfig \cube(0,0)|arlb|/ >->` >->`>`>/<1500,1500>[A`B`C`D;f`g`h`k]% (300,300)|arlb|/>`>`>`>/<400,400>[A'`B'`C'`D';f'`g'`h'`k']% |mmmm|/<-`<-`<-`<-/[\alpha`\beta`\gamma`\delta] \efig$$ \end{verbatim} gives the somewhat misshapen diagram $$\bfig \cube(0,0)|arlb|/ >->` >->`>`>/<1500,1500>[A`B`C`D;f`g`h`k]% (300,300)|arlb|/>`>`>`>/<400,400>[A'`B'`C'`D';f'`g'`h'`k']% |mmmm|/<-`<-`<-`<-/[\alpha`\beta`\gamma`\delta] \efig$$ because the parameters were oddly chosen. The defaults center the squares. I discovered accidently, while debugging the cube that what I though was an out-of-range choice of parameters would produce an offset cube: \begin{verbatim} $$\bfig \cube|arlb|/ >->` >->`>`>/<1000,1000>[A`B`C`D;f`g`h`k]% (400,400)|arlb|/>`>`>`>/<900,900>[A'`B'`C'`D';f'`g'`h'`k']% |rrrr|/<-`<-`<-`<-/[\alpha`\beta`\gamma`\delta] \efig$$ \end{verbatim} gives $$\bfig \cube|arlb|/ >->` >->`>`>/<1000,1000>[A`B`C`D;f`g`h`k]% (400,400)|arlb|/>`>`>`>/<900,900>[A'`B'`C'`D';f'`g'`h'`k']% |r`r`r`r|/<-`<-`<-`<-/[\alpha`\beta`\gamma`\delta] \efig$$ In homological algebra one often has a $3\times3$ diagram, with or without 0's on the margins. There is a macro to do that: \begin{verbatim} $$\bfig \iiixiii(0,0)|aammbblmrlmr|/>`>`>`>`>`>`>`>`>`>`>`>/<500,500>% {'5436}<400,400>[A'`B'`C'`A`B`C`A''`B''`C'';f'`g'`f`g`f''`g''`u`v`w`u'`v'`w'] \efig$$ \end{verbatim} that gives $$\bfig \iiixiii(0,0)|aammbblmrlmr|/>`>`>`>`>`>`>`>`>`>`>`>/<500,500>% {'5436}<400,400>[A'`B'`C'`A`B`C`A''`B''`C'';f'`g'`f`g`f''`g''`u`v`w`u'`v'`w'] \efig$$ Here is the explanation. The arrow parameters are not given in the usual order, but rather first all the horizontal arrows and then all the vertical ones, each in their usual order. The nodes are given in the usual order. The fifth parameter is the octal number 5436 (In \TeX, the \verb+'+ introduces octal numbers and \verb+"+ introduces hexadecimal numbers) which corresponds to the binary number 101,100,011,110 that describes the distribution of the 0's around the margins. The same results would have occurred if the number had been "B1E or the decimal number 2846. Note that the positioning parameters ignore the 0's so that it is the lower left node that appears at the position \verb.(x,y).. As usual, there are defaults \begin{verbatim} $$\bfig \iiixiii[A'`B'`C'`A`B`C`A''`B''`C'';f'`g'`f`g`f''`g''`u`v`w`u'`v'`w'] \efig$$ $$\bfig \iiixiii% {'5436}[A'`B'`C'`A`B`C`A''`B''`C'';f'`g'`f`g`f''`g''`u`v`w`u'`v'`w'] \efig$$ $$\bfig \iiixiii{'5436}<250,450>[A'`B'`C'`A`B`C`A''`B''`C'';% f'`g'`f`g`f''`g''`u`v`w`u'`v'`w'] \efig$$ \end{verbatim} $$\bfig \iiixiii[A'`B'`C'`A`B`C`A''`B''`C'';f'`g'`f`g`f''`g''`u`v`w`u'`v'`w'] \efig$$ $$\bfig \iiixiii% {'5436}[A'`B'`C'`A`B`C`A''`B''`C'';f'`g'`f`g`f''`g''`u`v`w`u'`v'`w'] \efig$$ $$\bfig \iiixiii{'5436}<250,450>[A'`B'`C'`A`B`C`A''`B''`C'';% f'`g'`f`g`f''`g''`u`v`w`u'`v'`w'] \efig$$ \subsection*{Empty placement and moving labels} The label placements within \verb+|p|+ is valid only for \verb+x = a,b,r,l,m+. If you use any other value (or leave it empty) the label entry is ignored, but you can use any valid \xypic\ label, as described in Figure 13 of the reference manual. One place you might want to use this is for the placement of the labels along an arrow. In \xypic\ the default placement of the label is midway between the midpoints of the nodes. If the two nodes are of widely different sizes, this can result in strange placements; therefore I always place them midway along the arrow. However, as the following illustrates, this can be changed. \begin{verbatim} $$\bfig \morphism(0,900)||/@{->}^<>(0.7){f}/<800,0>[A^B\times B^C\times C`C;] \morphism(0,600)||/@{->}^<(0.7){f}/<800,0>[A^B\times B^C\times C`C;] \morphism(0,300)||/@{->}^>(0.7){f}/<800,0>[A^B\times B^C\times C`C;] \morphism(0,0)||/@{->}^(0.7){f}/<800,0>[A^B\times B^C\times C`C;] \efig$$ \end{verbatim} which produces $$\bfig \morphism(0,900)||/@{->}^<>(0.7){f}/<800,0>[A^B\times B^C\times C`C;] \morphism(0,600)||/@{->}^<(0.7){f}/<800,0>[A^B\times B^C\times C`C;] \morphism(0,300)||/@{->}^>(0.7){f}/<800,0>[A^B\times B^C\times C`C;] \morphism(0,0)||/@{->}^(0.7){f}/<800,0>[A^B\times B^C\times C`C;] \efig$$ Here is the explanation. The label placement argument is empty (it cannot be omitted) and the arrow entry is empty. However, placing \verb+^(0.7){f}+ inside the arrow shape places the label \verb+f+ 7/10 of the way between the nodes. Unmodified, this places it 7/10 of the way between the centers of the nodes. This may be modified by \verb+<+, which moves the first (here the left) reference point to the beginning of the arrow, \verb+>+ which moves the second reference point to the end of the arrow, or by both, which moves both reference points. In most cases, you will want both. Incidentally, \verb+-+ is a synonym for the sequence \verb+<>(.5)+ and that is the default placement in my package. Here are some more examples that illustrates the special sequence \verb+\hole+ used in conjunction with \verb+|+ that implements \verb+m+ as well as the fact that these things can be stacked. For more details, I must refer you to the reference manual. \begin{verbatim} $$\bfig \morphism(0,600)||/@{->}|-\hole/<800,0>[A^B\times B^C\times C`C;] \morphism(0,300)||/@{->}|-\hole^<>(.7)f/<800,0>[A^B\times B^C\times C`C;] \morphism(0,0)||/@{->}|-\hole^<>(.7)f_<>(.3)g/<800,0>[A^B\times B^C\times C`C;] \efig$$ \end{verbatim} produces $$\bfig \morphism(0,600)||/@{->}|-\hole/<800,0>[A^B\times B^C\times C`C;] \morphism(0,300)||/@{->}|-\hole^<>(.7)f/<800,0>[A^B\times B^C\times C`C;] \morphism(0,0)||/@{->}|-\hole^<>(.7)f_<>(.3)g/<800,0>[A^B\times B^C\times C`C;] \efig$$ Here is another version of the cube we looked at above, using these special placements and \verb+\hole+'s to break some lines and make it neater. \begin{verbatim} $$\bfig \cube|arlb|/@{ >->}^<>(.6){f}` >->`@{>}_<>(.4){h}`>/% <1000,1000>[A`B`C`D;`g``k]% (400,400)|axxb|/>`@{>}|(.33)\hole^<>(.6){g'}`>`@{>}% |(.67)\hole_<>(.4){k'}/<900,900>[A'`B'`C'`D';f'``h'`]% |rrrr|/<-`<-`<-`<-/[\alpha`\beta`\gamma`\delta] \efig$$ \end{verbatim} $$\bfig \cube|arlb|/@{ >->}^<>(.6){f}` >->`@{>}_<>(.4){h}`>/% <1000,1000>[A`B`C`D;`g``k]% (400,400)|axl|/>`@{>}|(.33)\hole^<>(.6){g'}`>`% @{>}|(.67)\hole_<>(.4){k'}/<900,900>[A'`B'`C'`D';f'``h'`]% |rrrr|/<-`<-`<-`<-/[\alpha`\beta`\gamma`\delta] \efig$$ This one is probably worth saving as a template. Note that the \verb+\hole+'s by reference to the center of the nodes. That way they will always miss hitting the arrows no matter what the size of the node. If the nodes are unusually large, the cube may be magnified using \verb+\scalefactor+. \subsection*{Inline macros} Here we illustrate a few of the macros for inline---or displayed---equations the package contains. In each case, the macro may have a superscript or subscript or both (in which case the superscript must come first) and the arrow(s) grow long enough to hold the super- or subscript. If you type\par\noindent \verb+$A\to B\to^f C\to_g D\to^h_{{\rm Hom}(X,Y)} E$+, you get $A\to B\to^f C\to_g D\to^h_{{\rm Hom}(X,Y)} E$. Similarly, the macro \verb+\toleft+ reverses the arrows. The remaining macros of this sort are \verb+\mon+ which gives a monic arrow, \verb+\epi+ which gives an epic arrow, \verb+\two+ that gives a pair of arrows, as well as leftwards pointing versions, \verb+\monleft+, \verb+\epileft+, and \verb+twoleft+ of each of them. Here is one more example: \begin{verbatim} $A\twoleft B\twoleft^f C\twoleft_g D\twoleft^h_{{\rm Hom}(X,Y)} E$ \end{verbatim} gives $A\twoleft B\twoleft^f C\twoleft_g D\twoleft^h_{{\rm Hom}(X,Y)} E$. There is an almost unlimited variety of such procedures possible. The ones that are provided can be used as templates to define new ones with, say, curved arrows or three arrows or whatever a user might have need of. \subsection*{2-arrows} There is a macro for making 2-arrows of a fixed size, but varying orientation. They should be put at the appropriate position in a diagram. The two parameters are two integers \verb+dx+ and \verb+dy+ whose ratio is the slope of the arrow. They need not be relatively prime, but arithmetic overflow could occur if they are too large. Note that although \verb+(dx,dy)+ and \verb+(-dx,-dy)+ describe the same slope, the arrows point in opposite directions. Here is a sampler \begin{verbatim} $$\bfig \place(0,0)[\twoar(1,0)] \place(200,0)[\twoar(0,1)] \place(400,0)[\twoar(1,1)] \place(600,0)[\twoar(0,-1)] \place(800,0)[\twoar(1,2)] \place(1000,0)[\twoar(1,3)] \place(1200,0)[\twoar(1,-3)] \place(1400,0)[\twoar(-3,1)] \place(1600,0)[\twoar(-1,-3)] \place(1800,0)[\twoar(255,77)] \efig$$ \end{verbatim} $$\bfig \place(0,0)[\twoar(1,0)] \place(200,0)[\twoar(0,1)] \place(400,0)[\twoar(1,1)] \place(600,0)[\twoar(0,-1)] \place(800,0)[\twoar(1,2)] \place(1000,0)[\twoar(1,3)] \place(1200,0)[\twoar(1,-3)] \place(1400,0)[\twoar(-3,1)] \place(1600,0)[\twoar(-1,-3)] \place(1800,0)[\twoar(255,77)] \efig$$ Here is little amusement. \begin{verbatim} $$\bfig \square/@3{->}`~)`=o`--x/[A`B`C`D;```] \place(400,100)[\twoar(-1,-1)] \place(100,400)[\twoar(1,1)] \morphism(500,500)||/{*}.{*}/<-500,-500>[B`C;] \efig$$ \end{verbatim} $$\bfig \square/@3{->}`~)`=o`--x/[A`B`C`D;```] \place(400,100)[\twoar(-1,-1)] \place(100,400)[\twoar(1,1)] \morphism(500,500)||/{*}.{*}/<-500,-500>[B`C;] \efig$$ \subsection*{Diagram from TTT} The last example is a complicated diagram from TTT. If you have the documentation from the old diagram macros (or the errata from TTT), you can see how much easier it is to describe this diagram with these macros. Note the use of \verb+\scalefactor+ to change the default length from 500 to 700 that made it unnecessary to specify the scales on the squares and triangles. \begin{verbatim} $$\bfig \scalefactor{1.4}% \qtriangle(0,1000)/>`>`/[TT`T`TTT';\mu`TT\eta'`]% \btriangle(500,1000)/`>`@<-14\ul>/[T`TTT'`TT';`T\eta`T\sigma]% \morphism(0,1500)|l|/>/<0,-1000>[TT`TT'T;T\eta'T]% \square(500,500)|ammx|/@<14\ul>`>`>`/[TTT'`TT'`TT'TT'`TT'T';% \mu T'`T\eta'TT'`T\eta'T'`]% \morphism(1000,1000)|r|/>/<500,-500>[TT'`TT';\hbox{\rm id}]% \square/>`>``>/[TT'T`TT'TT'`T'T`T'TT';TT'T\eta'`\sigma T``T'T\eta']% \square(500,0)|ammb|[TT'TT'`TT'T'`T'TT'`T'T';% TT'\sigma`\sigma TT'`\sigma T'`T'\sigma T']% \square(1000,0)/>``>`>/[TT'T'`TT'`T'T'`T';T\mu'``\sigma`\mu']% \place(500,1250)[1]\place(215,1000)[2]\place(750,750)[3]% \place(215,250)[4]\place(750,250)[5]\place(1140,750)[6]% \place(1250,250)[7]% \efig$$ \end{verbatim} $$\bfig\label{TTTdiag} \scalefactor{1.4}% \qtriangle(0,1000)/>`>`/[TT`T`TTT';\mu`TT\eta'`]% \btriangle(500,1000)/`>`@<-14\ul>/[T`TTT'`TT';`T\eta`T\sigma]% \morphism(0,1500)|l|/>/<0,-1000>[TT`TT'T;T\eta'T]% \square(500,500)|ammx|/@<14\ul>`>`>`/[TTT'`TT'`TT'TT'`TT'T';\mu T'`% T\eta'TT'`T\eta'T'`]% \morphism(1000,1000)|r|/>/<500,-500>[TT'`TT';\hbox{\rm id}]% \square/>`>``>/[TT'T`TT'TT'`T'T`T'TT';TT'T\eta'`\sigma T``T'T\eta']% \square(500,0)|ammb|[TT'TT'`TT'T'`T'TT'`T'T';TT'\sigma`\sigma TT'% `\sigma T'`T'\sigma T']% \square(1000,0)/>``>`>/[TT'T'`TT'`T'T'`T';T\mu'``\sigma`\mu']% \place(500,1250)[1]\place(215,1000)[2]\place(750,750)[3]% \place(215,250)[4]\place(750,250)[5]\place(1140,750)[6]% \place(1250,250)[7]% \efig$$ \end{document} From rrosebru@mta.ca Thu May 3 09:33:27 2001 -0300 Return-Path: Received: (from Majordom@localhost) by mailserv.mta.ca (8.11.1/8.11.1) id f43BhpX18409 for categories-list; Thu, 3 May 2001 08:43:51 -0300 (ADT) X-Authentication-Warning: mailserv.mta.ca: Majordom set sender to cat-dist@mta.ca using -f To: Category Mailing List Subject: categories: Re: Limits References: Reply-To: Andrej.Bauer@andrej.com From: Andrej Bauer Date: 02 May 2001 19:10:56 +0200 In-Reply-To: Tobias Schroeder's message of "Wed, 2 May 2001 15:04:00 +0200 (CEST)" Message-ID: Lines: 50 User-Agent: Gnus/5.0807 (Gnus v5.8.7) XEmacs/21.1 (Capitol Reef) MIME-Version: 1.0 Content-Type: text/plain; charset=us-ascii Sender: cat-dist@mta.ca Precedence: bulk Status: O X-Status: X-Keywords: X-UID: 8 Tobias Schroeder writes: > So I'd be very grateful for answers to one of the following: > - Can the limit of a sequence of real numbers be expressed > as a categorical limit (of course it can if the sequence is > monotone, but what if it is not)? With a little bit of cheating, you can use domain theory to express the limit as a sequence as a _colimit_ in a partially ordered set. Let D be the partial order consisting of all the closed intervals, including singletons [a,a], ordered by reverse inclusion. We can embed R into D by mapping it to the maximal elements a |---> [a,a], and under a suitable topology on D (the Scott topology), this is a topological embedding--purists may want to throw in R as the smallest element to obtain an honest continuous domain. Let x_i be a Cauchy sequence of real numbers. To say that x_i is a Cauchy sequence is to say that there exist numbers d_i such that (1) For j >= i, the interval [x_i - d_i, x_i + d_i] contains [x_j + d_j, x_j + d_j]. (2) The numbers d_i become arbitrarily small: for every k there is i such that for all j >= i, d_i < 1/k. (Exercise for your students: show that this is equivalent to the usual definition of Cauchy sequence.) In terms of the partial order D, (1) says that the intervals [x_i - d_i, x_i + d_i] form an increasing sequence. Every increasing sequence in D has a supremum, because an intersection of a nested sequence of closed intervals is a closed interval, so let [u,v] = sup_i [x_i - d_i, x_i + d_i] By (2), we get that u = v, and we have obtained the limit of the sequence (x_i) as a supremum. Supremums are the _colimits_ in a partial order. If you prefer limits, you can stand on your head. I do not see how to get by without using the _evidence_ that (x_i) is a Cauchy sequence, i.e., the numbers d_i. This is intuitionistic mathematics creeping in, which is just as well. > - Why have people chosen the term "limit" in category theory? > (And, by the way, who has defined it first?) I am way too young to know the answer to this. Andrej From rrosebru@mta.ca Thu May 3 09:36:02 2001 -0300 Return-Path: Received: (from Majordom@localhost) by mailserv.mta.ca (8.11.1/8.11.1) id f43BgwE31822 for categories-list; Thu, 3 May 2001 08:42:58 -0300 (ADT) X-Authentication-Warning: mailserv.mta.ca: Majordom set sender to cat-dist@mta.ca using -f Date: Wed, 2 May 2001 13:02:36 -0400 (EDT) From: Peter Freyd Message-Id: <200105021702.f42H2aT18744@saul.cis.upenn.edu> To: categories@mta.ca Subject: categories: Re: Limits Sender: cat-dist@mta.ca Precedence: bulk Status: O X-Status: X-Keywords: X-UID: 9 Tobias Schroeder asks: - Can the limit of a sequence of real numbers be expressed as a categorical limit (of course it can if the sequence is monotone, but what if it is not)? A good question. I have no answer, only a similar (and ancient) question: is there a setting in which adjoint operators on Hilbert spaces can be seen to be examples of adjoint functors between categories? As for his second question: - Why have people chosen the term "limit" in category theory? (And, by the way, who has defined it first?) In the beginning, the only diagrams that had limits were "nets", that is, diagrams based on directed posets. I believe it was Norman Steenrod in his dissertation who first used the term. Before his dissertation the Cech cohomology of a space was defined only as the numberical invarients that arose as a limit of a directed set of such invariants. It was Steenrod who perceived that Cech cohomology could be defined as an abelian group. For that he needed to invent the notion of a limit of a directed diagram of groups. In the 50s the fact that one didn't need the diagram to be directed was considered startling. At least two of us tried to avoid the word "limit" in this more general setting. Jim Lambek was pushing "inf" and "sup", a suggestion I wish I had heard. Not having heard it, I was pushing "left root" and "right root" (one was, after all, supplying a root to a generalized tree. sort of). All to no avail. So now we have "finite limits" and "finitely continuous". From rrosebru@mta.ca Thu May 3 15:31:32 2001 -0300 Return-Path: Received: (from Majordom@localhost) by mailserv.mta.ca (8.11.1/8.11.1) id f43I4pF03260 for categories-list; Thu, 3 May 2001 15:04:51 -0300 (ADT) X-Authentication-Warning: mailserv.mta.ca: Majordom set sender to cat-dist@mta.ca using -f From: Martin Escardo MIME-Version: 1.0 Content-Type: text/plain; charset=us-ascii Content-Transfer-Encoding: 7bit Date: Thu, 3 May 2001 13:59:08 +0100 (BST) To: Category Mailing List Subject: categories: re: Limits In-Reply-To: References: X-Mailer: VM 6.43 under 20.4 "Emerald" XEmacs Lucid Message-ID: <15089.14134.867261.350412@henry.cs.bham.ac.uk> Sender: cat-dist@mta.ca Precedence: bulk Status: O X-Status: X-Keywords: X-UID: 10 Tobias Schroeder writes: > - Can the limit of a sequence of real numbers be expressed > as a categorical limit (of course it can if the sequence is > monotone, but what if it is not)? I think I have an answer to this question (without cheating). It may be well known or wrong (I haven't carefully checked the details, but I believe that they are correct). Given a metric space X with distance function d, construct a category, also called X, as follows. The objects of the category X are the points of the space X. An element of the hom-set X(x,y) is a triple (r,x,y) with r a real number such that d(x,y)<=r. The composite of the arrows r:x->y and s:y->z is the arrow s+r:x->z. This is well defined by virtue of the triangle inequality d(x,z)<=d(x,y)+d(y,z). By virtue of the condition d(x,x)=0, we have identities. Notice that all arrows are mono. Of course, because the category X is small and it is not a preordered set, it doesn't have all limits. But some limits do exist. CLAIM: Let x_n be a sequence of points of X, and, for each n, let the arrow r_n:x_{n+1}->x_n be d(x_n,x_{n+1}). If the sum of r_k over k>=0 exists, then this omega^op-diagram has a categorical limit. The source of the limiting cone is the metric limit l of the sequence. The projection p_n:l->x_n is the sum of r_k over k>=n. If q_n:m->x_n is another cone, then the mediating map u:l->m exists (and will be automatically unique), because, by definition of cone and of our category, q_n will have to be bigger than r_n, and then u=q_n-r_n does the job. Remarks. (1) For any given Cauchy sequence, one can construct an equivalent Cauchy sequence for which the assumption in the second sentence of the claim fails. Using classical logic, for any given Cauchy sequence, one can construct an equivalent Cauchy sequence for which the assumption holds. (2) In (some flavours of) constructive mathematics, the notion of a Cauchy sequence "with fixed rate of convergence" is taken as basic. This often is taken to mean that d(x_n,x_n+1)<=c^n for a fixed c with 0Y is called non-expansive if d(fx,fx')<=d(x,x'). If the natural numbers are metrized by d(m,n)=c^min(m,n) for m/=n, to get a space N, then such a Cauchy sequence is just a non-expansive map N->X. It converges if and only if the non-expansive map has a non-expansive extension to N_{infty}, the metric completion of N (which, topologically, is the one-point compactification of N). And non-expansive maps are functors---see (3) below. (3) Recall that a map f:X->Y is called lipschitz if there is a constant c for which d(fx,fx')<=c.d(x,x'). A lipschitz map f:X->Y gives rise to a functor f:X->Y defined by f(r:x->x')=c.r:f(r)->f(x'). That is, the object part is given by the map itself, and the arrow part is given by multiplication with the lipschitz coefficient. (4) We have taken the arrows r_n to be d(x_n,x_{n+1}). But actually any choice of arrows does the job, provided the sum of r_k over k>=0 is finite. (5) Other two conditions for the distance function of a metric space, which were not used in the definition of the category X, are (i) d(x,y)=0 implies x=y, and (ii) d(x,y)=d(y,x). By the first, our category is skeletal. By the second, it is selfdual. Of course, people have considered generalized metric spaces in which these are not assumed to hold. See, for example, Lawvere's paper "Metric spaces, generalized logic, and closed categories", in which he regards a generalized metric space X as an enriched category with X(x,y)=d(x,y) (so he has hom-numbers instead of hom-sets). Here we have hom-sets (of numbers). MHE From rrosebru@mta.ca Fri May 4 09:11:07 2001 -0300 Return-Path: Received: (from Majordom@localhost) by mailserv.mta.ca (8.11.1/8.11.1) id f44BYMH31876 for categories-list; Fri, 4 May 2001 08:34:22 -0300 (ADT) X-Authentication-Warning: mailserv.mta.ca: Majordom set sender to cat-dist@mta.ca using -f Date: Fri, 4 May 2001 10:21:21 +0100 (BST) From: "Dr. P.T. Johnstone" To: categories@mta.ca Subject: categories: pullbacks of local operators Message-ID: MIME-Version: 1.0 Content-Type: TEXT/PLAIN; charset=US-ASCII X-Scanner: exiscan *14vblu-0005ZL-00*egzk/I/1bqw* http://duncanthrax.net/exiscan/ Sender: cat-dist@mta.ca Precedence: bulk Status: O X-Status: X-Keywords: X-UID: 11 Dear Colleagues, I've recently come across a result in elementary topos theory which looks as if it ought to be well known, but which I've never seen before. So I'm writing to ask whether anyone else knows about it. The context for the result is as follows: given a geometric morphism f: E' --> E and a local operator (or Lawvere--Tierney topology, if you prefer) j on E, it's well known that one can construct a local operator j' on E' such that sh_j'(E') -----> sh_j(E) | | | | v f v E' -----------> E is a pullback. To do this, let J >--> \Omega be the subobject classified by j, and form the smallest local operator j' for which the corresponding J' contains the image of f^*J >--> f^*\Omega ---> \Omega' (the second factor being the canonical comparison map, which classifies f^*(true)). See "Topos Theory", Example 3.59(iii). The result in question is that, for any f and J, the object J' is simply the upward closure in \Omega' of the image of the above composite; equivalently, that the classifying map of the upward closure of the image is always a local operator (in particular, that it's idempotent). When I first came across evidence that this might be true, a couple of months ago, I was inclined to disbelieve it, on the grounds that if it were true we'd surely have known it for twenty years or so. However ... I now have (separate, and completely different) proofs that it holds in several particular cases, including the case in which f is an open map, and that in which f is a closed inclusion. But it's also clear that the class of f's for which it holds is closed under composition, and using Artin glueing one can factor any f as a closed inclusion followed by an open map; so it's true for all f. Has anyone seen this result before? In particular, does anyone have a "uniform" proof of it that works for all f? If so, please let me know. Peter Johnstone From rrosebru@mta.ca Fri May 4 09:11:11 2001 -0300 Return-Path: Received: (from Majordom@localhost) by mailserv.mta.ca (8.11.1/8.11.1) id f44BWnH32431 for categories-list; Fri, 4 May 2001 08:32:49 -0300 (ADT) X-Authentication-Warning: mailserv.mta.ca: Majordom set sender to cat-dist@mta.ca using -f Message-ID: <3AF1E676.918BC691@kestrel.edu> Date: Thu, 03 May 2001 16:15:02 -0700 From: Dusko Pavlovic X-Mailer: Mozilla 4.72 [en] (X11; U; SunOS 5.5.1 sun4u) X-Accept-Language: en MIME-Version: 1.0 To: Category Mailing List Subject: categories: Re: Limits References: <15089.14134.867261.350412@henry.cs.bham.ac.uk> Content-Type: text/plain; charset=us-ascii Content-Transfer-Encoding: 7bit Sender: cat-dist@mta.ca Precedence: bulk Status: O X-Status: X-Keywords: X-UID: 12 > Tobias Schroeder writes: > > - Can the limit of a sequence of real numbers be expressed > > as a categorical limit (of course it can if the sequence is > > monotone, but what if it is not)? > > I think I have an answer to this question (without cheating). It may > be well known or wrong (I haven't carefully checked the details, but I > believe that they are correct). the view of (quasi)metric spaces as R+-categories with the hom-objects d(x,y) goes back to lawvere's "metric spaces, generalized logic and closed categories" from 1973. the cauchy completeness of a space was identified with what came to be known as the cauchy completeness of the corresponding category (see kelly's book on enriched categories, or francis borceux handbook). and cauchy completeness of a category amounts to the existence of certain absolute (co)limits: eg over Set, Ab, Cat... to splitting idempotents (which can be done by taking (co)equalizers with id). -- dusko From rrosebru@mta.ca Fri May 4 09:14:24 2001 -0300 Return-Path: Received: (from Majordom@localhost) by mailserv.mta.ca (8.11.1/8.11.1) id f44BXgl01062 for categories-list; Fri, 4 May 2001 08:33:42 -0300 (ADT) X-Authentication-Warning: mailserv.mta.ca: Majordom set sender to cat-dist@mta.ca using -f Date: Thu, 3 May 2001 16:38:18 -0700 (PDT) Message-Id: <200105032338.f43NcI203820@math-cl-n03.ucr.edu> From: jdolan@math.ucr.edu To: categories@mta.ca Subject: categories: Re: Limits Sender: cat-dist@mta.ca Precedence: bulk Status: O X-Status: X-Keywords: X-UID: 13 |A good question. I have no answer, only a similar (and ancient) |question: is there a setting in which adjoint operators on Hilbert |spaces can be seen to be examples of adjoint functors between |categories? i may as well state the obvious (not necesarily right) answer to this: no, not quite. rather, what seems to be going on is that the phenomenon of adjoint linear operators is, in yetter's terminology, a sort of decategorification of the phenomenon of adjoint functors. decategorification is generally a somewhat destructive process, destroying the morphisms between objects, and since the morphisms are so intrinsic to the definition of adjoint functor it seems too much to hope for that the decategorified phenomenon of adjoint linear operators could actually qualify as a special case of adjoint functors. there are suggestive indications, though, that all of the really interesting special cases of adjoint linear operators in physics, for example, are decategorifications of interesting pairs of adjoint functors. (for example so-called "creation and annihilation operators on fock space" have categorified analogs that live on a categorified analog of fock space whose objects/vectors are something like joyal's "species of structure".) so roughly: the general phenomenon of adjoint linear operators is technically probably not quite a genuine special case of adjoint functors. the actual interesting special cases of adjoint linear operators, however, are often seen to be mere shadows of more interesting cases of adjoint functors. From rrosebru@mta.ca Fri May 4 14:02:48 2001 -0300 Return-Path: Received: (from Majordom@localhost) by mailserv.mta.ca (8.11.1/8.11.1) id f44GbQA18369 for categories-list; Fri, 4 May 2001 13:37:26 -0300 (ADT) X-Authentication-Warning: mailserv.mta.ca: Majordom set sender to cat-dist@mta.ca using -f From: Steve Stevenson MIME-Version: 1.0 Content-Type: text/plain; charset=us-ascii Content-Transfer-Encoding: 7bit Message-ID: <15090.44521.498991.254345@merlin.cs.clemson.edu> Date: Fri, 4 May 2001 09:26:01 -0400 (EDT) To: categories@mta.ca Subject: categories: Please help set up course X-Mailer: VM 6.72 under 21.1 (patch 11) "Carlsbad Caverns" XEmacs Lucid Sender: cat-dist@mta.ca Precedence: bulk Status: RO X-Status: X-Keywords: X-UID: 14 Good morning, y'all: I really need some help in setting up a reading course. The course is for computer science majors and faculty who are very interested and motivated but lack a strong background in mathematics. The goal the group has is to be able to read the denotational semantics literature. Now, as you know, this is quite an undertaking. How can I quickly give them some background? My first thought is to tie categorical concepts to something they all might know. Is there an article, book, or sequence of same that takes a less than formal approach to concepts and then comes back with the formality? I call this a "rosetta stone" approach. I've read Pierce's *Basic Category Theory for Computer Scientists*. What I think I need is something that would serve as an introduction (to even Pierce) as to why computer scientists should want to know about pushouts, pullbacks, and some of the other structures that don't seen to be obviously necessary. Any guidance would be gratefully accepted! best regards, steve From rrosebru@mta.ca Fri May 4 14:05:40 2001 -0300 Return-Path: Received: (from Majordom@localhost) by mailserv.mta.ca (8.11.1/8.11.1) id f44GcA700181 for categories-list; Fri, 4 May 2001 13:38:10 -0300 (ADT) X-Authentication-Warning: mailserv.mta.ca: Majordom set sender to cat-dist@mta.ca using -f X-Authentication-Warning: triples.math.mcgill.ca: barr owned process doing -bs Date: Fri, 4 May 2001 10:49:42 -0400 (EDT) From: Michael Barr X-Sender: barr@triples.math.mcgill.ca To: Categories list Subject: categories: Re: diaxydoc.tex In-Reply-To: <200105041348.KAA11287@rjwood.cs.dal.ca> Message-ID: MIME-Version: 1.0 Content-Type: TEXT/PLAIN; charset=US-ASCII Sender: cat-dist@mta.ca Precedence: bulk Status: O X-Status: X-Keywords: X-UID: 15 I have discovered that a blank line in version 3 of the diagram documentation that I sent out the other day has caused errors. Here is the correct paragraph: In homological algebra one often has a $3\times3$ diagram, with or without 0's on the margins. There is a macro to do that: \begin{verbatim} $$\bfig \iiixiii(0,0)|aammbblmrlmr|/>`>`>`>`>`>`>`>`>`>`>`>/<500,500>% {'5436}<400,400>[A'`B'`C'`A`B`C`A''`B''`C'';f'`g'`f`g`f''`g''`u`v`w`u'`v'`w'] \efig$$ \end{verbatim} that gives $$\bfig \iiixiii(0,0)|aammbblmrlmr|/>`>`>`>`>`>`>`>`>`>`>`>/<500,500>% {'5436}<400,400>[A'`B'`C'`A`B`C`A''`B''`C'';f'`g'`f`g`f''`g''`u`v`w`u'`v'`w'] \efig$$ Sorry about that. From rrosebru@mta.ca Fri May 4 20:40:07 2001 -0300 Return-Path: Received: (from Majordom@localhost) by mailserv.mta.ca (8.11.1/8.11.1) id f44NGiI11870 for categories-list; Fri, 4 May 2001 20:16:44 -0300 (ADT) X-Authentication-Warning: mailserv.mta.ca: Majordom set sender to cat-dist@mta.ca using -f Date: Fri, 4 May 2001 14:04:36 -0700 (PDT) Message-Id: <200105042104.f44L4al17252@math-cl-n03.ucr.edu> From: jdolan@math.ucr.edu To: categories@mta.ca Subject: categories: Re: Limits Sender: cat-dist@mta.ca Precedence: bulk Status: O X-Status: X-Keywords: X-UID: 16 i wrote: |phenomenon of adjoint linear operators is, in yetter's terminology, a |sort of decategorification of the phenomenon of adjoint functors. now that i think about i guess it was crane rather than yetter who started using the term "categorification". is it correct that lawvere and schanuel use the term "objectification" (or something like that) to mean pretty much the same thing as what crane meant by "categorification"? i think i might actually prefer "objectification" here but i mostly hang out near sub-communities where "categorification" has caught on to a certain extent. From rrosebru@mta.ca Sun May 6 09:25:28 2001 -0300 Return-Path: Received: (from Majordom@localhost) by mailserv.mta.ca (8.11.1/8.11.1) id f46Bqjb14218 for categories-list; Sun, 6 May 2001 08:52:45 -0300 (ADT) X-Authentication-Warning: mailserv.mta.ca: Majordom set sender to cat-dist@mta.ca using -f Mime-Version: 1.0 X-Sender: street@hera.mpce.mq.edu.au Message-Id: In-Reply-To: <200105042104.f44L4al17252@math-cl-n03.ucr.edu> References: <200105042104.f44L4al17252@math-cl-n03.ucr.edu> Date: Sun, 6 May 2001 10:26:04 +1000 To: categories@mta.ca From: Ross Street Subject: categories: Re: Limits Content-Type: text/plain; charset="us-ascii" ; format="flowed" Sender: cat-dist@mta.ca Precedence: bulk Status: O X-Status: X-Keywords: X-UID: 17 I very much agree with James Dolan's response to the question of comparing categorical limits and adjoint functors with their abstract counterparts in analysis. Other words that have been used for "objectification" and "categorification" are "laxification" and "identity breaking". The original questions were a bit like asking: "Is the plus in an abelian group a categorical coproduct?" Lots of abelian groups can arise by taking isomorphism classes and using a categorical coproduct: but then we lose the beautiful universal property. Along the same lines, I enjoy bicategories, with coproducts in their homcategories (preserved by composition), much more than additive categories. Not only is every global coproduct in such a bicategory also a global product, but the projections from the global products are right adjoint to the coprojections into the coproduct. Ross From rrosebru@mta.ca Mon May 7 13:35:50 2001 -0300 Return-Path: Received: (from Majordom@localhost) by mailserv.mta.ca (8.11.1/8.11.1) id f47FgxI20215 for categories-list; Mon, 7 May 2001 12:42:59 -0300 (ADT) X-Authentication-Warning: mailserv.mta.ca: Majordom set sender to cat-dist@mta.ca using -f Message-Id: <200105071037.MAA21066@irmast2.u-strasbg.fr> Date: Mon, 7 May 2001 12:37:35 +0200 (MET DST) From: Philippe Gaucher Reply-To: Philippe Gaucher Subject: categories: preprint : Investigating The Algebraic Structure of Dihomotopy Types To: categories@mta.ca MIME-Version: 1.0 Content-Type: TEXT/plain; charset=us-ascii Content-MD5: UD46CYDXyqWX9V/UPodX7w== X-Mailer: dtmail 1.3.0 @(#)CDE Version 1.3.5 SunOS 5.7 sun4u sparc Sender: cat-dist@mta.ca Precedence: bulk Status: RO X-Status: X-Keywords: X-UID: 18 Title : Investigating The Algebraic Structure of Dihomotopy Types Abstract : This presentation is the sequel of a paper published in GETCO'00 proceedings where a research program to construct an appropriate algebraic setting for the study of deformations of higher dimensional automata was sketched. This paper will be focused precisely on detailing some of its aspects. The main idea is that the category of homotopy types can be embedded in a new category of dihomotopy types, the embedding being realized by the Globe functor. In this latter category, isomorphism classes of objects are exactly higher dimensional automata up to deformations leaving invariant their computer scientific properties as presence or not of deadlocks (or everything similar or related). Some hints to study the algebraic structure of dihomotopy types are given, in particular a rule to decide whether a statement/notion concerning dihomotopy types is or not the lifting of another statement/notion concerning homotopy types. This rule does not enable to guess what is the lifting of a given notion/statement, it only enables to make the verification, once the lifting has been found. Comment : submitted to getco'01. expository paper. URL : http://www-irma.u-strasbg.fr/~gaucher/dihomotopy.ps.gz http://www-irma.u-strasbg.fr/~gaucher/dihomotopy.pdf From rrosebru@mta.ca Mon May 7 13:39:09 2001 -0300 Return-Path: Received: (from Majordom@localhost) by mailserv.mta.ca (8.11.1/8.11.1) id f47FhfI19151 for categories-list; Mon, 7 May 2001 12:43:41 -0300 (ADT) X-Authentication-Warning: mailserv.mta.ca: Majordom set sender to cat-dist@mta.ca using -f Date: Mon, 7 May 2001 01:05:03 +0200 (CEST) From: Anders Kock To: categories@mta.ca Subject: categories: 75 PSSL Message-ID: MIME-Version: 1.0 Content-Type: TEXT/PLAIN; charset=US-ASCII Sender: cat-dist@mta.ca Precedence: bulk Status: RO X-Status: X-Keywords: X-UID: 19 75th PSSL - First announcement The 75th meeting of the Peripatetic Seminar on Sheaves and Logic will be held at the Institut Mittag-Leffler, Stockholm, on the week-end of 9-10 June 2001. As usual, we invite contributions from anyone interested in the application of categorical and sheaf theoretic methods in logic and related areas. If you wish to attend, please complete the attached registration form and return it to kock@ml.kva.se or palmgren@math.uu.se as soon as possible, and in any case before the end of May. The number of participants is for physical reasons limited to 30 Further information and a provisional programme will be circulated about a week before the meeting. The meeting may be seen as a satelitte event of the Logic Year, which is taking place at the Mittag-Leffler Institute; a number of colleagues with interest in Sheaves and Logic are scheduled to be present in Stockholm during the period, in the context of the Logic Year. Anders Kock Erik Palmgren Dana Scott Registration Form Name: Address: e-mail: I intend to come to the 75th meeting of the PSSL. I should like to give a talk lasting about ...minutes, entitled ....................................... PS. If you are interested in getting help or advice concerning Hotel or Guesthouse accomodation, please contact A.K. or E.P as soon as possible, at kock@ml.kva.se or palmgren@math.uu.se From rrosebru@mta.ca Sat May 5 18:19:20 2001 -0300 Return-Path: Received: (from Majordom@localhost) by mailserv.mta.ca (8.11.1/8.11.1) id f45KULh13721 for categories-list; Sat, 5 May 2001 17:30:21 -0300 (ADT) X-Authentication-Warning: mailserv.mta.ca: Majordom set sender to cat-dist@mta.ca using -f Message-ID: <3AF44D5A.7D18BA9C@email.unc.edu> Date: Sat, 05 May 2001 14:58:34 -0400 From: jim stasheff X-Mailer: Mozilla 4.7 [en] (WinNT; I) X-Accept-Language: en MIME-Version: 1.0 To: categories@mta.ca Subject: categories: Re: Limits References: <200105021702.f42H2aT18744@saul.cis.upenn.edu> Content-Type: text/plain; charset=us-ascii Content-Transfer-Encoding: 7bit Sender: cat-dist@mta.ca Precedence: bulk Status: O X-Status: X-Keywords: X-UID: 20 The category of finite sets and isomorphisms versus the category with objects 1,2,...,n,... and the symmetric groups \Sigma_n as morphisms The category of `modules' over one is equivalent to The category of `modules' over the other Is this somewhere in the literature or just folk lore? Maybe for one n at a time?? thanks jim From rrosebru@mta.ca Tue May 8 09:01:33 2001 -0300 Return-Path: Received: (from Majordom@localhost) by mailserv.mta.ca (8.11.1/8.11.1) id f48BGUI18048 for categories-list; Tue, 8 May 2001 08:16:30 -0300 (ADT) X-Authentication-Warning: mailserv.mta.ca: Majordom set sender to cat-dist@mta.ca using -f From: Jiri Adamek Message-Id: <200105071236.OAA09189@lisa.iti.cs.tu-bs.de> Subject: categories: connected functors To: categories@mta.ca Date: Mon, 7 May 2001 14:36:35 +0200 (MET DST) X-Mailer: ELM [version 2.5 PL2] MIME-Version: 1.0 Content-Type: text/plain; charset=us-ascii Content-Transfer-Encoding: 7bit Sender: cat-dist@mta.ca Precedence: bulk Status: O X-Status: X-Keywords: X-UID: 21 Connected Functors Peter Johnstone has asked during the last PSSL for a characterization of functors p: E -> B which are "connected" in the sense that the functor Set^B -> Set^E of composition with p is fully faithful. We have found two necesary and sufficient conditions; in the following E and B are arbitrary small categories. Theorem 1. A functor p: E -> B is connected iff every object X of B is an absolute limit of the diagram of all arrows X -> p(Z) for Z ranging through E . Theorem 2. A functor p: E -> B is connected iff for every morphism x: X -> X' of B the category of all factorizations of x through objects of p[E] is connected. More precisely, in Thm 1 we form the diagram of all arrows X -> p(Z) and all E-morphisms whose p-image forms a commutative triangle in B. Then X is equipped with a canonical cone of that diagram; this cone is requested to be an absolute limit. In Thm 2 we consider the category of all triples (Z,q,m) where Z is an object of E and m,q are morphisms of B with x = q.m (and morphisms between these triples are the E-morphisms whose p-images form two commutative triangles in B ). Connectedness of that category has been, for the case of x = id , observed as a necessary condition by Peter. J. Adamek, R. El Bashir, M. Sobral and J. Velebil xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx alternative e-mail address (in case reply key does not work): J.Adamek@tu-bs.de xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx alternative e-mail address (in case reply key does not work): J.Adamek@tu-bs.de xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx From rrosebru@mta.ca Tue May 8 09:09:25 2001 -0300 Return-Path: Received: (from Majordom@localhost) by mailserv.mta.ca (8.11.1/8.11.1) id f48BEEu22654 for categories-list; Tue, 8 May 2001 08:14:14 -0300 (ADT) X-Authentication-Warning: mailserv.mta.ca: Majordom set sender to cat-dist@mta.ca using -f Date: Mon, 7 May 2001 14:16:11 +1000 (EST) From: maxk@maths.usyd.edu.au (Max Kelly) Message-Id: <200105070416.f474GBI212924@milan.maths.usyd.edu.au> To: categories@mta.ca Subject: categories: Re: Please help set up course Sender: cat-dist@mta.ca Precedence: bulk Status: RO X-Status: X-Keywords: X-UID: 22 Dear Steve, My first hurried thoughts recall two books: that of Bob Walters, `Categories and Computer Science' (Cambridge University Press, 1991) and that of Lawvere-Schanuel's course at Buffalo, `Conceptual Mathematics: a First Introduction to Categories' (CUP, 1997). Max. From rrosebru@mta.ca Wed May 9 08:50:05 2001 -0300 Return-Path: Received: (from Majordom@localhost) by mailserv.mta.ca (8.11.1/8.11.1) id f49B8HS20808 for categories-list; Wed, 9 May 2001 08:08:17 -0300 (ADT) X-Authentication-Warning: mailserv.mta.ca: Majordom set sender to cat-dist@mta.ca using -f X-Authentication-Warning: triples.math.mcgill.ca: barr owned process doing -bs Date: Tue, 8 May 2001 09:45:42 -0400 (EDT) From: Michael Barr X-Sender: barr@triples.math.mcgill.ca To: Categories list Subject: categories: Final version of diagxy Message-ID: MIME-Version: 1.0 Content-Type: TEXT/PLAIN; charset=US-ASCII Sender: cat-dist@mta.ca Precedence: bulk Status: RO X-Status: X-Keywords: X-UID: 23 The final version is available as a diagxy.zip from ftp.math.mcgill.ca by anonymous ftp in pub/barr/. This includes the diagxy.tex and diaxydoc.tex. The former differs from the third version only in trivial ways (some extra \ignorespaces were added to try to prevent extraneous spaces from causing problems). The opening pages of the documentation are different, but the examples are all the same. From rrosebru@mta.ca Wed May 9 08:52:17 2001 -0300 Return-Path: Received: (from Majordom@localhost) by mailserv.mta.ca (8.11.1/8.11.1) id f49BL2N27918 for categories-list; Wed, 9 May 2001 08:21:02 -0300 (ADT) X-Authentication-Warning: mailserv.mta.ca: Majordom set sender to cat-dist@mta.ca using -f Message-ID: <00cf01c0d707$84d0e740$5997fac1@pavilion> Reply-To: "Catherine Piliere" From: "Catherine Piliere" To: Subject: categories: LACL 2001 - Call for Participation Date: Mon, 7 May 2001 16:54:22 +0200 MIME-Version: 1.0 Content-Type: text/plain; charset="iso-8859-1" X-Priority: 3 X-MSMail-Priority: Normal X-Mailer: Microsoft Outlook Express 5.00.2615.200 X-MimeOLE: Produced By Microsoft MimeOLE V5.00.2615.200 Content-Transfer-Encoding: 8bit X-MIME-Autoconverted: from quoted-printable to 8bit by mailserv.mta.ca id f47F65b23052 Sender: cat-dist@mta.ca Precedence: bulk Status: RO X-Status: X-Keywords: X-UID: 24 ************************************************************************** --- Please accept our apologies for multiple copies --- --- Thank you in advance to circulate among interested people--- ************************************************************************** Call for Participation - Program LACL 2001 4th International Conference on LOGICAL ASPECTS OF COMPUTATIONAL LINGUISTICS June 27 -- 29, 2001 Le Croisic (on the ocean coast, nearby Nantes), France Deadline for early registration: June 1st http://www.irisa.fr/LACL2001 ************************************************************************** *** Practical information, schedule, on-line registration: http://www.irisa.fr/LACL2001 http://www.irisa.fr/manifestations/2001/LACL2001 *** Contact: Christele Soulas csoulas@irisa.fr Elisabeth Lebret lebret@irisa.fr *************************************************************************** -- LACL 2001 PROGRAM -- *************************************************************************** --- Invited speakers ----------------------------- Geoffrey K. PULLUM, Barbara C. SCHOLZ : On the distinction between Model-theoretic and Generative-enumerative syntactic frameworks Michael MOORTGAT : Structural Reasoning in Categorial Learning Mark STEEDMAN : Reconciling Type-Logical and Combinatory Extensions of Categorial Grammar --- Contributed papers ------------------------- M. A. ALONSO, E. DE LA CLERGERIE, M. VILARES : A formal definition of Bottom-up Embedded Push-Down Automata and their tabulation technique D. BARGELLI, J. LAMBEK : An algebraic Approach to French Sentence Structure P. BOTTONI, B. MEYER, K. MARRIOTT, F. PARISI PRESICCE : Deductive Parsing of Visual Languages W. BUSZKOWSKI : Lambek Grammars based on Pregroups C. CASADIO, J. LAMBEK : An Algebraic Analysis of Clitic Pronouns in Italian C. COSTA FLORENCIO : Consistent Identification in the Limit of any of the Classes k-Valued is NP-hard A.DIKOVSKY : Polarized Non-projective Dependency Grammars A. FORET : Mixing Deduction and Substitution in Lambek Categorial Grammars, some investigations C. FOX, S. LAPPIN : Framework for the Hyperintensional Semantics of Natural Language with Two Implementations H. HARKEMA : A Characterization of Minimalist Languages T. LAGER, J. NIVRE : Part of Speech Tagging from a Logical Point of View J. MICHAELIS : Transforming Linear Context-Free Rewriting Systems into Minimalist Grammars E. STABLER : Recognizing Head Movement J. VILLADSEN : Combinators for Paraconsistent Attitudes J. VILLANEAU, J.-Y. ANTOINE, O. RIDOUX : Combining Syntax and Semantical Knowledge for Semantic Analysis of Spoken Language R. ZUBER : Atomicity of Some Categorially Polyvalent Modifiers --- Panel discussion : Logic in Contemporary Linguistics and Computational Linguistics ************************************************************************ *** Organizers: IRISA (INRIA, CNRS, Université de Rennes 1, INSA) IRIN (Université de Nantes) *** Sponsors: France Telecom R&D Xerox Loire Atlantique Pays de la Loire Ville de Nantes Université de Rennes 1 Université de Nantes *** Book and journal exhibition: Elsevier Hermes Kluwer Lincom Europa MIT Press Springer-Verlag World Scientific Publishing Company *** Other events in computational linguistics in France, early July: 2-5 july, Tours, TALN & RECITAL 2001: http://www.li.univ-tours.fr/taln-recital-2001/ 6-11 july, Toulouse, ACL 2001: http://www.irit.fr/ACTIVITES/EQ_ILPL/aclWeb/acl2001.html *************************************************************************** From rrosebru@mta.ca Wed May 9 20:21:44 2001 -0300 Return-Path: Received: (from Majordom@localhost) by mailserv.mta.ca (8.11.1/8.11.1) id f49MudY16315 for categories-list; Wed, 9 May 2001 19:56:39 -0300 (ADT) X-Authentication-Warning: mailserv.mta.ca: Majordom set sender to cat-dist@mta.ca using -f Message-Id: <200105092217.f49MHW315771@imgw1.cpsc.ucalgary.ca> Date: Wed, 9 May 2001 16:12:51 -0600 (MDT) From: robin@cpsc.ucalgary.ca Subject: categories: Idempotent monoidal monads ... To: categories@mta.ca MIME-Version: 1.0 Content-Type: TEXT/plain; charset=us-ascii Sender: cat-dist@mta.ca Precedence: bulk Status: O X-Status: X-Keywords: X-UID: 25 Recently I stumbled on the following: I find it hard to believe that they are not well-known facts. I would be grateful for references ... (a) The conditions for the Kleisli category of a monoidal monad to be closed (left/right) w.r.t the induced tensor when the original category is (left/right) closed. (b) The fact that, in the above situation, when the monad is idempotent the Kleisli category is always closed. With thanks in advance -robin (Robin Cockett) From rrosebru@mta.ca Thu May 10 08:38:23 2001 -0300 Return-Path: Received: (from Majordom@localhost) by mailserv.mta.ca (8.11.1/8.11.1) id f4AAwqm21469 for categories-list; Thu, 10 May 2001 07:58:52 -0300 (ADT) X-Authentication-Warning: mailserv.mta.ca: Majordom set sender to cat-dist@mta.ca using -f Message-ID: <3AF9FA78.9968DFEE@kestrel.edu> Date: Wed, 09 May 2001 19:18:32 -0700 From: Dusko Pavlovic X-Mailer: Mozilla 4.72 [en] (X11; U; SunOS 5.5.1 sun4u) X-Accept-Language: en MIME-Version: 1.0 To: categories@mta.ca Subject: categories: Re: Limits References: <200105032338.f43NcI203820@math-cl-n03.ucr.edu> Content-Type: text/plain; charset=us-ascii Content-Transfer-Encoding: 7bit Sender: cat-dist@mta.ca Precedence: bulk Status: O X-Status: X-Keywords: X-UID: 26 Peter Freyd wrote: > A good question. I have no answer, only a similar (and ancient) > question: is there a setting in which adjoint operators on Hilbert > spaces can be seen to be examples of adjoint functors between > categories? probably not, but the they seem to be instances of the same general structure. (it is simple, pretty old, and i am sure many have noticed it, but since no one mentioned it, here it goes.) let U : Cat ---> CAT be the embedding of small categories in all, and let Y: Cat^op ---> CAT map each small category A to the presheaves Psh(A). now look at the (pseudo)comma category U/Y. each category A is represented in it by the yoneda embedding A-->Psh(A). the morphisms between A-->Psh(A) and B --> Psh(B) are exactly the pairs of adjoint functors between A and B. on the other hand, let I: Vec---> Vec be the identity functor, and let * : Vec^op ---> Vec take a vector space V to its dual V*. look at the comma category I/*. each hilbert space V is represented in it by the obvious linear map V-->V*. the morphisms between V-->V* and W-->W* are exactly the adjoint pairs of operators between V and W. playing around a bit, these two comma categories can be thought of as Chu(CAT,Set) and Chu(Vec,R) respectively. so both sorts of adjunctions are the instances of the chu morphisms. they are the chu morphisms on the "representation" objects, in the form X --> R^X, where R is the dualizing object. -- dusko PS infact, one could start from Chu(SET,Set), and define categories as the profunctors A-->Set^A which form a monoid with respect to the profunctor composition. you'd get only the object part of the adjoint functors as the morphisms of this chu, but the arrow part follows from the adjunction (i think). now can we characterize hilbert spaces in a similar way within Chu(Vec,R)? this seems to be a completely different kind of question. in particular, it is possible to define "profunctors" with respect to R or C, like we did with respect to Set, and we can compose them, but hilbert spaces do not seem to be monoids with respect to this composition, at least the way it occurs to me. if there is no such composition that they are, then hilbert spaces are like R-enriched graphs, rather than categories. From rrosebru@mta.ca Sat May 12 09:53:23 2001 -0300 Return-Path: Received: (from Majordom@localhost) by mailserv.mta.ca (8.11.1/8.11.1) id f4CCOFg21437 for categories-list; Sat, 12 May 2001 09:24:15 -0300 (ADT) X-Authentication-Warning: mailserv.mta.ca: Majordom set sender to cat-dist@mta.ca using -f Message-Id: <5.0.2.1.2.20010511124058.00aca8e0@mailbox.syr.edu> X-Sender: lglewis@mailbox.syr.edu X-Mailer: QUALCOMM Windows Eudora Version 5.0.2 Date: Fri, 11 May 2001 13:13:44 -0400 To: categories@mta.ca From: Gaunce Lewis Subject: categories: question about enriched category theory Mime-Version: 1.0 Content-Type: text/plain; charset="us-ascii"; format=flowed Sender: cat-dist@mta.ca Precedence: bulk Status: O X-Status: X-Keywords: X-UID: 27 Assume that V is a symmetric monoidal closed category and that A and B are categories enriched over V which have tensors. Let me denote the tensor of an object v of V and an object a of A by v \ten a Assume also that F is a functor from the underlying ordinary category A_0 of A to the underlying category B_0 of B. If F were enriched over V, then there would be a natural map f : v \ten Fa --> F(v \ten a) describing the behavior of F on tensors. However, assume only that F is a functor on the underlying categories. It seems to me that, if there is a well-behaved natural map f of the above form for all v in V and a in A, then F ought to be enriched over V. It is easy to construct from f the map that ought to be the enrichment for F. The trick is to decide what properties f must have in order to ensure that the putative enrichment really works. Is this written up somewhere? Along the same lines, suppose now that F and G are enriched functors from A to B with the associated maps f : v \ten Fa --> F(v \ten a) and g : v \ten Ga --> G(v \ten a) describing their behavior on tensors. Assume also that t is an ordinary natural tranformation between the ordinary functors F_0 and G_0 underlying F and G. There is an obvious diagram relating t, f, and g, and it seems that this diagram ought to commute if t is an enriched natural transformation. In fact, it seems that the commutativity of this diagram ought to be equivalent to t being enriched over V. Is this written down anywhere? Thanks for any help on this, Gaunce From rrosebru@mta.ca Sat May 12 09:53:23 2001 -0300 Return-Path: Received: (from Majordom@localhost) by mailserv.mta.ca (8.11.1/8.11.1) id f4CCMOA06630 for categories-list; Sat, 12 May 2001 09:22:24 -0300 (ADT) X-Authentication-Warning: mailserv.mta.ca: Majordom set sender to cat-dist@mta.ca using -f Message-ID: <3AFACA37.EC0906E0@bangor.ac.uk> Date: Thu, 10 May 2001 18:04:55 +0100 From: Ronnie Brown X-Mailer: Mozilla 4.76 [en] (Win98; U) X-Accept-Language: en MIME-Version: 1.0 To: categories@mta.ca Subject: categories: Paris seminar Content-Type: text/plain; charset=iso-8859-1 Content-Transfer-Encoding: 8bit X-MIME-Autoconverted: from quoted-printable to 8bit by mailserv.mta.ca id f4AH4vb11262 Sender: cat-dist@mta.ca Precedence: bulk Status: O X-Status: X-Keywords: X-UID: 28 Paris Seminar Notice: http://www.di.ens.fr/~longo/geocogni.html Groupe de Travail GÉOMÉTRIE ET COGNITION (Giuseppe LONGO*, Jean PETITOT°, Bernard TEISSIER*) 30 Mai : R. Brown (Math., Univ. of Wales) "The intuitions of higher dimensional algebra for the study of structured space." 16h, SALLE U ou V, étage -2 , Dépts. de Math. et d'Informatique, ENS, 45, Rue D'Ulm, 75005 Paris: ABSTRACT One definition of Higher Dimensional Algebra is that it is about algebraic structures whose operations are partially defined under geometric conditions, and whose axioms are defined by the geometry - so for example one considers composing squares and cubes in various directions. This allows for a more detailed transition from geometry to algebra. One overall aim is to provide new tools for local-to-global problems by the procedure `algebraic inverses to subdivision'. The pursuit of this aim has led to a range of new algebraic structures, new understanding and computations in algebraic topology, as well as new tools for concurrency problems. Its potential relevance to this seminar is the speculative idea that a mathematics `on a line' cannot be adequate for describing the complex modular and hierarchical interactions of the brain. So Higher Dimensional Algebra can perhaps open out new modelling possibilities for future development. For more background, see http://www.bangor.ac.uk/~mas010/hdaweb2.htm The structure of the talk will be 1. Origins and intuitions 2. Landmark theorems: these are of the type (a) equivalent descriptions of the algebraic structures (b) gluing (colimit) theorems (c) realisation of algebra by spaces 3. Computational issues 4. The future? (The aim is to give an impression of this area for a more general audience, and so consideration of `weak structures' and many other applications will be omitted.) Ronnie Brown From rrosebru@mta.ca Sat May 12 09:53:28 2001 -0300 Return-Path: Received: (from Majordom@localhost) by mailserv.mta.ca (8.11.1/8.11.1) id f4CCNUs03857 for categories-list; Sat, 12 May 2001 09:23:30 -0300 (ADT) X-Authentication-Warning: mailserv.mta.ca: Majordom set sender to cat-dist@mta.ca using -f Date: Thu, 10 May 2001 19:22:25 +0200 From: Jerome Durand-Lose Message-Id: <200105101722.f4AHMPA10810@bianca.inria.fr> To: categories@mta.ca Subject: categories: STACS 2002 Call for papers Sender: cat-dist@mta.ca Precedence: bulk Status: O X-Status: X-Keywords: X-UID: 29 ============================================================== We apologize for multiple copies of this call for papers ============================================================== +--------------------+ | | | STACS 2002 | | | +--------------------+ 19th International Symposium on Theoretical Aspects of Computer Science Antibes Juan-les-Pins, France March 14--16 2002 http://www.inria.fr/stacs2002 SCOPE: Authors are invited to submit papers presenting original and unpublished research on theoretical aspects of computer science. Typical areas include (but are not limited to): * Algorithms and data structures, including: parallel and distributed algorithms, computational geometry, cryptography, algorithmic learning theory; * Automata and formal languages; * Computational and structural complexity; * Logic in computer science, including: semantics, specification, and verification of programs, rewriting and deduction; * Current challenges, for example: theory, models, and algorithms for biological computing, quantum computing, mobile and net computing. SUBMISSIONS: Authors are invited to submit a draft of a full paper (5-12 pages, the title page must contain a classification of the topic covered, preferably using the list of topics above). The paper should contain a succinct statement of the issues and of their motivation, a summary of the main results, and a brief explanation of their significance, accessible to non-specialist readers. Proofs omitted due to space constraints must be put into an appendix to be read by the program committee members at their discretion. Electronic submission is highly recommended. In case of problems with access to internet, it is possible to submit 6 copies of the draft (plus 1 copy of the appendix) and 15 copies of a one page abstract to the chairperson of the program committee. Detailed information is available on the web site. IMPORTANT DATES: Deadline for submission: September 14, 2001 Notification to authors: November 21, 2001 Final version: December 14, 2001 Symposium: March 14--16, 2002 PROCEEDINGS: Accepted papers will be published in the proceedings of the Symposium (Lecture Notes in Computer Science, Springer-Verlag). Simultaneous submission to other conferences with published proceedings is not allowed. PROGRAM COMMITTEE: H. Alt (Berlin) Co-Chair H. Buhrman (Amsterdam) B. Chlebus (Warsaw) T. Erlebach (Zuerich) A. Ferreira (Sophia-Antipolis) Chair H. Ganzinger (Saarbruecken) D. Lugiez (Marseille) Y. Metivier (Bordeaux) C. Moore (Albuquerque / Santa Fe) A. Muscholl (Paris) G. Pucci (Padova) G. Schnitger (Frankfurt) T. Schwentick (Jena) D. Trystram (Grenoble) B. Voecking (Saarbruecken) KEYNOTE SPEAKER: M.O. Rabin (Harvard) INVITED SPEAKERS: G. Dowek (Rocquencourt) C. Scheideler (Baltimore) CONFERENCE CHAIR: Afonso Ferreira CNRS et I3S INRIA Sophia-Antipolis 2004, route des Lucioles BP 93 F-06902 Sophia-Antipolis France ORGANIZING COMMITTEE CHAIR: J. Durand-Lose (Nice) E-ADDRESS: stacs@sophia.inria.fr WEB SITE: http://www.inria.fr/stacs2002 ==== please post and distribute ==== From rrosebru@mta.ca Wed May 16 22:37:59 2001 -0300 Return-Path: Received: (from Majordom@localhost) by mailserv.mta.ca (8.11.1/8.11.1) id f4H1AD313125 for categories-list; Wed, 16 May 2001 22:10:13 -0300 (ADT) X-Authentication-Warning: mailserv.mta.ca: Majordom set sender to cat-dist@mta.ca using -f Date: Tue, 15 May 2001 13:08:08 +0200 (MET DST) From: Message-Id: <200105151108.NAA15073@kodder.math.uu.nl> To: categories@mta.ca Subject: categories: preprint: Ordered PCA's and Realizability Toposes X-Sun-Charset: US-ASCII Sender: cat-dist@mta.ca Precedence: bulk Status: O X-Status: X-Keywords: X-UID: 30 Paper available: P.J.W. Hofstra and J. van Oosten, Ordered PCA's and Realizability Toposes http://www.math.uu.nl/people/jvoosten/papers.html Abstract: The concept of Ordered PCA (Partial Combinatory Algebra) is defined; it is a generalization of ordinary PCA's. The construction of Realizability Toposes for OPCA's is straightforward. Two 2-categories OPCA and OPCA+ are defined, OPCA+ being a lluf subcategory of OPCA. Both have a 2-monad I on them. It is shown that the category of realizability triposes over opca's with Set-indexed exact functors is equivalent to the Kleisli category of I on OPCA, whereas the category of realizabiloity triposes with geometric morphisms is the Kleisli category for I on OPCA+. This extends and analyzes results in the theses of Pitts and Longley. As an application we obtain an elegant tripos presentation of Menni's chain of toposes, constructed as exact completions. From rrosebru@mta.ca Wed May 16 22:37:59 2001 -0300 Return-Path: Received: (from Majordom@localhost) by mailserv.mta.ca (8.11.1/8.11.1) id f4H1FRk06043 for categories-list; Wed, 16 May 2001 22:15:27 -0300 (ADT) X-Authentication-Warning: mailserv.mta.ca: Majordom set sender to cat-dist@mta.ca using -f X-Received: from zent.mta.ca (zent.mta.ca [138.73.101.4]) by mailserv.mta.ca (8.11.1/8.11.1) with SMTP id f4FB02b21889 for ; Tue, 15 May 2001 08:00:04 -0300 (ADT) X-Received: FROM queen.math.muni.cz BY zent.mta.ca ; Tue May 15 08:00:45 2001 -0300 X-Received: by queen.math.muni.cz (Postfix, from userid 23025) id B22B982F7; Tue, 15 May 2001 13:59:43 +0200 (CEST) Subject: categories: preprint: Left-determined model categories and universal homotopy theories To: categories@mta.ca Date: Tue, 15 May 2001 13:59:43 +0200 (CEST) X-Mailer: ELM [version 2.4ME+ PL69 (25)] MIME-Version: 1.0 Content-Type: text/plain; charset=US-ASCII Content-Transfer-Encoding: 7bit Message-Id: <20010515115943.B22B982F7@queen.math.muni.cz> From: rosicky@math.muni.cz (Jiri Rosicky) Sender: cat-dist@mta.ca Precedence: bulk Status: O X-Status: X-Keywords: X-UID: 31 The following paper is available at http://www.math.yorku.ca/Who/Faculty/Tholen/research.html J.Rosicky and W.Tholen, Left-determined model categories and universal homotopy theories Abstract: We say that a model category is left-determined if the weak equivalences are generated (in a suitable sense) by the cofibrations. While the model category of simplicial sets is not left-determined, we show that its non-oriented variant, the category of symmetric simplicial sets (in the sense of Lawvere and Grandis) carries a natural left-determined model category structure. This is used to give another and, as we believe, simpler proof of a recent result of D. Dugger about universal homotopy theories. From rrosebru@mta.ca Wed May 16 22:39:25 2001 -0300 Return-Path: Received: (from Majordom@localhost) by mailserv.mta.ca (8.11.1/8.11.1) id f4H1HFo03850 for categories-list; Wed, 16 May 2001 22:17:15 -0300 (ADT) X-Authentication-Warning: mailserv.mta.ca: Majordom set sender to cat-dist@mta.ca using -f Importance: Normal X-Priority: 3 (Normal) Subject: categories: Re: Limits To: categories@mta.ca From: "Paul H Palmquist" Date: Wed, 16 May 2001 15:46:00 -0700 Message-ID: X-MIMETrack: Serialize by Router on RWSMTA10/SRV/Raytheon/US(Release 5.0.6a |January 17, 2001) at 05/16/2001 03:46:39 PM MIME-Version: 1.0 Content-type: text/plain; charset=us-ascii Sender: cat-dist@mta.ca Precedence: bulk Status: O X-Status: X-Keywords: X-UID: 32 Peter Freyd wrote: > A good question. I have no answer, only a similar (and ancient) > question: is there a setting in which adjoint operators on Hilbert > spaces can be seen to be examples of adjoint functors between > categories? I once answered a similar question. In 1974 or 1975, I published a paper "Adjoint functors induced by adjoint linear transformations" in the Proceedings of the AMS. The idea is that a pair of adjoint linear transformations between two linear topological vectorspaces, e.g., a special case is Hilbert spaces, naturally map to an adjoint pair of functors between the categories which are the lattices of closed subspaces, i.e., a galois connection. Cheers, Paul H. Palmquist Paul Palmquist @compuserve.com> on 05/16/2001 08:35:30 AM To: Paul Palmquist cc: Subject: categories: Re: Limits -------------Forwarded Message----------------- From: Dusko Pavlovic, INTERNET:dusko@kestrel.edu To: [unknown], INTERNET:categories@mta.ca Date: 5/10/01 4:29 AM RE: categories: Re: Limits Peter Freyd wrote: > A good question. I have no answer, only a similar (and ancient) > question: is there a setting in which adjoint operators on Hilbert > spaces can be seen to be examples of adjoint functors between > categories? probably not, but the they seem to be instances of the same general structure. (it is simple, pretty old, and i am sure many have noticed it, but since no one mentioned it, here it goes.) let U : Cat ---> CAT be the embedding of small categories in all, and let Y: Cat^op ---> CAT map each small category A to the presheaves Psh(A). now look at the (pseudo)comma category U/Y. each category A is represented in it by the yoneda embedding A-->Psh(A). the morphisms between A-->Psh(A) and B --> Psh(B) are exactly the pairs of adjoint functors between A and B. on the other hand, let I: Vec---> Vec be the identity functor, and let * : Vec^op ---> Vec take a vector space V to its dual V*. look at the comma category I/*. each hilbert space V is represented in it by the obvious linear map V-->V*. the morphisms between V-->V* and W-->W* are exactly the adjoint pairs of operators between V and W. playing around a bit, these two comma categories can be thought of as Chu(CAT,Set) and Chu(Vec,R) respectively. so both sorts of adjunctions are the instances of the chu morphisms. they are the chu morphisms on the "representation" objects, in the form X --> R^X, where R is the dualizing object. -- dusko PS infact, one could start from Chu(SET,Set), and define categories as the profunctors A-->Set^A which form a monoid with respect to the profunctor composition. you'd get only the object part of the adjoint functors as the morphisms of this chu, but the arrow part follows from the adjunction (i think). now can we characterize hilbert spaces in a similar way within Chu(Vec,R)? this seems to be a completely different kind of question. in particular, it is possible to define "profunctors" with respect to R or C, like we did with respect to Set, and we can compose them, but hilbert spaces do not seem to be monoids with respect to this composition, at least the way it occurs to me. if there is no such composition that they are, then hilbert spaces are like R-enriched graphs, rather than categories. ----------------------- Internet Header -------------------------------- Sender: cat-dist@mta.ca Received: from mailserv.mta.ca (mailserv.mta.ca [138.73.101.5]) by sphmgaae.compuserve.com (8.9.3/8.9.3/SUN-1.9) with ESMTP id HAA02263 for <76600.1050@compuserve.com>; Thu, 10 May 2001 07:29:48 -0400 (EDT) Received: (from Majordom@localhost) by mailserv.mta.ca (8.11.1/8.11.1) id f4AAwqm21469 for categories-list; Thu, 10 May 2001 07:58:52 -0300 (ADT) X-Authentication-Warning: mailserv.mta.ca: Majordom set sender to cat-dist@mta.ca using -f Message-ID: <3AF9FA78.9968DFEE@kestrel.edu> Date: Wed, 09 May 2001 19:18:32 -0700 From: Dusko Pavlovic X-Mailer: Mozilla 4.72 [en] (X11; U; SunOS 5.5.1 sun4u) X-Accept-Language: en MIME-Version: 1.0 To: categories@mta.ca Subject: categories: Re: Limits References: <200105032338.f43NcI203820@math-cl-n03.ucr.edu> Content-Type: text/plain; charset=us-ascii Content-Transfer-Encoding: 7bit Sender: cat-dist@mta.ca Precedence: bulk From rrosebru@mta.ca Thu May 17 00:43:45 2001 -0300 Return-Path: Received: (from Majordom@localhost) by mailserv.mta.ca (8.11.1/8.11.1) id f4H3OG919703 for categories-list; Thu, 17 May 2001 00:24:16 -0300 (ADT) X-Authentication-Warning: mailserv.mta.ca: Majordom set sender to cat-dist@mta.ca using -f Date: Wed, 16 May 2001 18:43:29 -0700 (PDT) From: mjhealy@redwood.rt.cs.boeing.com (Michael Healy 425-865-3123) Message-Id: <200105170143.SAA03635@lilith.rt.cs.boeing.com> To: categories@mta.ca Subject: categories: An application X-Sun-Charset: US-ASCII Sender: cat-dist@mta.ca Precedence: bulk Status: O X-Status: X-Keywords: X-UID: 33 A review of a paper I submitted to a neural network journal is taking awhile. In the meantime, for anyone who might be interested, there is a conference paper online with an overview of the content. It concerns a proposed mathematical semantic model for neural networks: M. J. Healy (2000) "Category Theory Applied to Neural Modeling and Graphical Representations", Proceedings of the International Joint Conference on Neural Networks (IJCNN2000), Como, Italy. It's available at http://cialab.ee.washington.edu/ . Click on "Publications", then "Selected Publications", and scroll down. The same site has a paper on topological semantics, the other part of the proposed model. Developing and applying it is a major part of my work right now, so I would welcome comments from anyone who might be interested. Regards, Mike Healy -- =========================================================================== e Michael J. Healy A FA ----------> GA (425)865-3123 | | FAX(425)865-2964 | | Ff | | Gf c/o The Boeing Company | | PO Box 3707 MS 7L-66 \|/ \|/ Seattle, WA 98124-2207 ' ' USA FB ----------> GB -or for priority mail- e "I'm a natural man." 2760 160th Ave SE MS 7L-66 B Bellevue, WA 98008 USA michael.j.healy@boeing.com -or- mjhealy@u.washington.edu ============================================================================ From rrosebru@mta.ca Fri May 18 01:03:49 2001 -0300 Return-Path: Received: (from Majordom@localhost) by mailserv.mta.ca (8.11.1/8.11.1) id f4I2DIZ19667 for categories-list; Thu, 17 May 2001 23:13:18 -0300 (ADT) X-Authentication-Warning: mailserv.mta.ca: Majordom set sender to cat-dist@mta.ca using -f Message-ID: <006501c0df13$fe6fb400$87657bc8@athlon> From: To: Subject: categories: Structure Preserving: Definition? Date: Thu, 17 May 2001 15:57:33 -0500 MIME-Version: 1.0 Content-Type: text/plain; charset="iso-8859-1" Content-Transfer-Encoding: 7bit X-Priority: 3 X-MSMail-Priority: Normal X-Mailer: Microsoft Outlook Express 6.00.2462.0000 X-MimeOLE: Produced By Microsoft MimeOLE V6.00.2462.0000 Sender: cat-dist@mta.ca Precedence: bulk Status: O X-Status: X-Keywords: X-UID: 34 Hello, I've sent the following message to sci.math, but haven't received a clear answer. I've also tried sci.math.research, but the moderator bounced the posting. Possibly someone here can help? Derek. =============================================== I'm working through the following paper, trying to learn a bit more about category theory: Matrices, Monads and the Fast Fourier Transform http://citeseer.nj.nec.com/jay93matrice.html I this paper, the author explains vectors in categorical notation: "Vectors are distinguished from lists because their length is given as part of their structure, represented by a morphism (function) #: VA -> N." What this means is that the morphism '#' will produce the length of vector. However, does this violate one of the requirements that a morphism must preserve the structure of an object? A vector is a sequence of elements, and an integer is only a single value. Does this mean that an integer has the same structure as a vector? Or does "structure preserving morphism" mean something different? Thanks, Derek. From rrosebru@mta.ca Sat May 19 00:51:41 2001 -0300 Return-Path: Received: (from Majordom@localhost) by mailserv.mta.ca (8.11.1/8.11.1) id f4J3NBG21106 for categories-list; Sat, 19 May 2001 00:23:11 -0300 (ADT) X-Authentication-Warning: mailserv.mta.ca: Majordom set sender to cat-dist@mta.ca using -f Message-Id: <4.1.20010518084716.009fb410@mail.oberlin.net> X-Sender: cwells@mail.oberlin.net X-Mailer: QUALCOMM Windows Eudora Pro Version 4.1 Date: Fri, 18 May 2001 08:49:36 -0400 To: categories@mta.ca From: Charles Wells Subject: categories: Re: Structure Preserving: Definition? In-Reply-To: <006501c0df13$fe6fb400$87657bc8@athlon> Mime-Version: 1.0 Content-Type: text/plain; charset="us-ascii" Sender: cat-dist@mta.ca Precedence: bulk Status: O X-Status: X-Keywords: X-UID: 35 The function # should not have been referred to as a morphism. It is an operation. Operations must be preserved by morphisms, but operations need not be morphisms themselves. (In fact a distributive law is a statement that some operation is a morphism with respect to another operation.) -Charles Wells >Hello, >I've sent the following message to sci.math, but haven't >received a clear answer. I've also tried sci.math.research, >but the moderator bounced the posting. Possibly someone >here can help? > >Derek. >=============================================== > >I'm working through the following paper, trying to learn a bit >more about category theory: > >Matrices, Monads and the Fast Fourier Transform >http://citeseer.nj.nec.com/jay93matrice.html > >I this paper, the author explains vectors in categorical >notation: > >"Vectors are distinguished from lists because their length >is given as part of their structure, represented by a morphism >(function) #: VA -> N." > >What this means is that the morphism '#' will produce the >length of vector. > >However, does this violate one of the requirements that a >morphism must preserve the structure of an object? A vector >is a sequence of elements, and an integer is only a single >value. Does this mean that an integer has the same structure >as a vector? > >Or does "structure preserving morphism" mean something >different? > >Thanks, > >Derek. > > > > > > Charles Wells, Emeritus Professor of Mathematics, Case Western Reserve University Affiliate Scholar, Oberlin College Send all mail to: 105 South Cedar St., Oberlin, Ohio 44074, USA. email: charles@freude.com. home phone: 440 774 1926. professional website: http://www.cwru.edu/artsci/math/wells/home.html personal website: http://www.oberlin.net/~cwells/index.html NE Ohio Sacred Harp website: http://www.oberlin.net/~cwells/sh.htm From rrosebru@mta.ca Sun May 20 00:43:40 2001 -0300 Return-Path: Received: (from Majordom@localhost) by mailserv.mta.ca (8.11.1/8.11.1) id f4K3HKx06062 for categories-list; Sun, 20 May 2001 00:17:20 -0300 (ADT) X-Authentication-Warning: mailserv.mta.ca: Majordom set sender to cat-dist@mta.ca using -f Mime-Version: 1.0 X-Sender: street@hera.mpce.mq.edu.au Message-Id: Date: Sat, 19 May 2001 18:28:55 +1000 To: categories@mta.ca From: Ross Street Subject: categories: Chair of Mathematics Content-Type: text/plain; charset="us-ascii" ; format="flowed" Sender: cat-dist@mta.ca Precedence: bulk Status: O X-Status: X-Keywords: X-UID: 36 Dear Category Theorists A Chair of Mathematics at Macquarie University was advertised today (Saturday) in the Sydney Morning Herald. I notice that it has not yet appeared on the appropriate Macquarie website: http://www.pers.mq.edu.au/ads/index.html But it should be there soon! The reference number for the job is 19139. The appointee "will be supported by a substantial start-up grant and a new lectureship in the Department." I would be very happy to hear from anyone genuinely interested, or of good suggestions for possible candidates. I would also like to point out that good opportunities now exist for postgraduate study in category theory at Macquarie. Australian students can be funded by Australian Postgraduate Awards (APA) as usual. However, new opportunities exist for international students to have their fees waived and obtain a living allowance comparable to the APA. Of course, these Scholarships are awarded competitively. See http://www.mq.edu.au/postgrad/awards.htm Our category group (CoACT) is eligible for RAACE awards: http://www.mq.edu.au/postgrad/schl/RAACE.htm I also believe there will be things called iMURS advertised soon which include the waiving of fees. http://www.mq.edu.au/international/graduate/ I would be happy to hear from, or of, prospective postgraduate students interested in working towards a PhD in category theory at Macquarie. Yours truly, Ross From rrosebru@mta.ca Sun May 20 00:43:40 2001 -0300 Return-Path: Received: (from Majordom@localhost) by mailserv.mta.ca (8.11.1/8.11.1) id f4K3Hpo01116 for categories-list; Sun, 20 May 2001 00:17:51 -0300 (ADT) X-Authentication-Warning: mailserv.mta.ca: Majordom set sender to cat-dist@mta.ca using -f X-Authentication-Warning: triples.math.mcgill.ca: barr owned process doing -bs Date: Sat, 19 May 2001 08:07:09 -0400 (EDT) From: Michael Barr X-Sender: barr@triples.math.mcgill.ca To: Categories list Subject: categories: Wells's reply Message-ID: MIME-Version: 1.0 Content-Type: TEXT/PLAIN; charset=US-ASCII Sender: cat-dist@mta.ca Precedence: bulk Status: O X-Status: X-Keywords: X-UID: 37 I unfortunately deleted Charles's reply to the question about dimension being an operation. But thinking about it I realized that dimension is not an operation in the theory of vector spaces either; It is not preserved by morphisms. For vector spaces, even finite dimensional ones, the existence of dimension is a theorem. But the original question was not about vector spaces, but about coordinate spaces. For which the only morphisms are square permutation matrices. And the distributive law does not say that multiplication is a morphism with respect to addition. It does say that multiplication by a fixed element (on the right or the left) is a morphism with respect to addition. But I don't think that an infinitary distributive law (say between infinite sups and infinite infs) can be stated in such a way at all. Michael From rrosebru@mta.ca Mon May 21 05:21:39 2001 -0300 Return-Path: Received: (from Majordom@localhost) by mailserv.mta.ca (8.11.1/8.11.1) id f4L7dZv29345 for categories-list; Mon, 21 May 2001 04:39:35 -0300 (ADT) X-Authentication-Warning: mailserv.mta.ca: Majordom set sender to cat-dist@mta.ca using -f To: categories@mta.ca Subject: categories: Re: Structure Preserving: Definition? In-Reply-To: Your message of "Thu, 17 May 2001 15:57:33 -0500" <006501c0df13$fe6fb400$87657bc8@athlon> References: <006501c0df13$fe6fb400$87657bc8@athlon> X-Mailer: Mew version 1.93b38 on XEmacs 21.1 (Acadia) Reply-To: cbj@it.uts.edu.au Mime-Version: 1.0 Content-Type: Text/Plain; charset=us-ascii Content-Transfer-Encoding: 7bit Message-Id: <20010521122102D.cbj@socs.uts.edu.au> Date: Mon, 21 May 2001 12:21:02 +1000 From: Barry Jay X-Dispatcher: imput version 980905(IM100) Lines: 63 Content-Transfer-Encoding: 7bit Content-Transfer-Encoding: 7bit Sender: cat-dist@mta.ca Precedence: bulk Status: O X-Status: X-Keywords: X-UID: 38 Dear Derek, since "Matrices, Monads and the Fast Fourier Transform" in the early 90's I've written a couple of other papers on semantics of datatypes. "A semantics for shape" considers more general datatypes than just vectors. "Data categories" is an attempt to embrace co-datatypes as well as datatypes. These, and other papers about the implications for computing, including the array programming language FISh are available from my web-site http://www-staff.it.uts.edu.au/~cbj May I add that we are stabilising a prototype of FISh2 which is altogether more expressive and simpler than FISh. We hope to release it shortly. Now let me address your particular question. you are concerned that the morphism #: VA -> N mapping a vector of A's to its length does not appear to preserve any structure, and so perhaps should not be a morphism at all. There are two aspects to the answer. First, the existence of this morphism is part of the definition of the object of vectors. Given an arrow A -->I we define the corresponding vectors by the pullback VA ---> LA | | | | NxI --> LI where L is the list functor, and then # is defined by composing VA -->NxI with the projection from NxI to N. If the ambient category is Set then such pullbacks exist and the function # is a well-defined function. The second point is that # can be thought of as the upper part of an arrow between arrows which maps a vector of A's to the corresponding vector of 1's VA ---> V1 isom N | | | | | | NxI --> Nx1 isom N I'd be happy to address any other questions you have privately. Yours, Barry Jay ************************************************************************* | Associate Professor C.Barry Jay, Phone: (61 2) 9514 1814 | | Associate Dean Fax: (61 2) 9514 1807 | | (Research, Policy and Planning) | | University of Technology, Sydney, e-mail: cbj@it.uts.edu.au | | P.O. Box 123 Broadway, 2007, | | Australia. http://www-staff.it.uts.edu.au/~cbj | ************************************************************************* From rrosebru@mta.ca Mon May 21 22:23:59 2001 -0300 Return-Path: Received: (from Majordom@localhost) by mailserv.mta.ca (8.11.1/8.11.1) id f4M10jF24767 for categories-list; Mon, 21 May 2001 22:00:45 -0300 (ADT) X-Authentication-Warning: mailserv.mta.ca: Majordom set sender to cat-dist@mta.ca using -f Date: Mon, 21 May 2001 14:44:03 +0200 (CEST) From: Anders Kock - Guest To: categories@mta.ca Subject: categories: preprint: Characterization of stacks of principal fibre bundles Message-ID: MIME-Version: 1.0 Content-Type: TEXT/PLAIN; charset=US-ASCII Sender: cat-dist@mta.ca Precedence: bulk Status: RO X-Status: X-Keywords: X-UID: 39 Anders Kock: Characterization of stacks of principal fibre bundles is available on the address http://www.ml.kva.se/preprints/meta/KockThu_May_17_12_51_36.rdf.html Abstract: Stacks of principal fibre bundles are stacks whose total category has binary products, and an atlas. This holds on any basis category equipped with a class of descent morphisms (the notions of atlas, stack, etc. refer to this class.) (Note: my permanent e-mail address is unchanged, kock@imf.au.dk) Anders K. From rrosebru@mta.ca Tue May 22 23:35:52 2001 -0300 Return-Path: Received: (from Majordom@localhost) by mailserv.mta.ca (8.11.1/8.11.1) id f4N27Ym18315 for categories-list; Tue, 22 May 2001 23:07:34 -0300 (ADT) X-Authentication-Warning: mailserv.mta.ca: Majordom set sender to cat-dist@mta.ca using -f X-Authentication-Warning: triples.math.mcgill.ca: barr owned process doing -bs Date: Tue, 22 May 2001 07:36:22 -0400 (EDT) From: Michael Barr X-Sender: barr@triples.math.mcgill.ca To: Categories list Subject: categories: diagxy Message-ID: MIME-Version: 1.0 Content-Type: TEXT/PLAIN; charset=US-ASCII Sender: cat-dist@mta.ca Precedence: bulk Status: RO X-Status: X-Keywords: X-UID: 40 An update of diagxy is now available as ftp.math.mcgill.ca//pub/barr/diagxy.zip. It fixes a couple of serious bugs (in more esoteric shapes), makes some minor improvements in the macros and adds and modifies the documentation, including clarifying the license to make it absolutely clear that there are no restrictions of use. In addition, I have corrected a couple of typos that Steve Bloom found. In addition, I recommend that you download the paper derfun.tex. This is a paper that I wrote last summer (and has been submitted for publication) that I have modified to use the new macros. The bug fixes and modifications were found in getting this paper looking right. From rrosebru@mta.ca Wed May 23 21:47:30 2001 -0300 Return-Path: Received: (from Majordom@localhost) by mailserv.mta.ca (8.11.1/8.11.1) id f4O0PDP04328 for categories-list; Wed, 23 May 2001 21:25:13 -0300 (ADT) X-Authentication-Warning: mailserv.mta.ca: Majordom set sender to cat-dist@mta.ca using -f From: street@ics.mq.edu.au Mime-Version: 1.0 X-Sender: street@hera.mpce.mq.edu.au Message-Id: Date: Wed, 23 May 2001 18:09:59 +1000 To: categories@mta.ca Subject: categories: Our Advertisement Sender: cat-dist@mta.ca Precedence: bulk Status: O X-Status: X-Keywords: X-UID: 41 MACQUARIE UNIVERSITY DIVISION OF INFORMATION AND COMMUNICATION SCIENCES Department of Mathematics Chair of Mathematics (Full-time (continuing)) Ref. 19139 Applications are invited for a Chair of Mathematics. The Department of Mathematics has an international reputation for research in analysis, category theory and number theory. The teaching program covers the range from undergraduate service teaching for science and business/economics degree majors, to mathematics majors and honours, and postgraduate research in mathematics. The multidisciplinary Division of Information and Communication Sciences brings together Mathematics, Physics, Computing and Electronics and offers exciting opportunities for the development of mathematics and its applications in information technology, physics, communications and business. The appointee will be a distinguished academic who will strengthen teaching and research in mathematics and its applications, lead the Department in the development and implementation of educational and research objectives, expand cooperation with other Departments in the Division and elsewhere in the University, and develop teaching and research links with the industry and business community. The appointment will provide an opportunity for growth and will be supported by a substantial start-up grant and a new lectureship in the Department. The appointee will be expected to be Head of Department from time to time. Essential criteria: A PhD or equivalent in mathematics; an outstanding international research reputation and strong publication record; demonstrated ability to attract research funding; extensive experience in research supervision; an accomplished teaching record; effective communication and administrative skills; a capacity for academic leadership through innovation, motivation and strategic thinking. Desirable criteria: Ability to identify and develop productive partnerships with the external community, or successful experience in curriculum reform and the development of flexible learning approaches in the delivery of the teaching program. Enquiries: Professor Jim Piper, Head of Division on phone +61 2 9850 9500 or e-mail Jim.Piper@mq.edu.au or Dr Rod Yager, Head of Department on +61 2 9850 8934 or fax +61 2 9850 8114 or e-mail rody@maths.mq.edu.au Further information is also available at http://www.math.mq.edu.au The position is available on a full-time (continuing) basis. Salary range: Level E (Professor) A$ 92,425 to A$96,861 per annum, plus superannuation. The University reserves the right to invite applications for any position, to leave the Chair unfilled, to make more than one appointment, and to make enquiries of any person regarding the candidate's suitability for appointment. Further information about the University, conditions of appointment and the method of application should be obtained from Ms Gaby Laudams on phone +61 2 98509725 or fax +61 2 9850 9748 or e-mail Gaby.Laudams@mq.edu.au An application package MUST be obtained prior to sending your application. Applicants should systematically address the selection criteria, and include a full curriculum vitae, evidence of academic qualifications and experience, and copies of their best three publications, which should be highlighted in the application. Applicants should also state their visa status, and provide the names and addresses (including e-mail address, telephone and fax numbers) of three academic and professional referees. Applications quoting the reference number should be forwarded to the Recruitment Manager, Personnel Office, Macquarie University, NSW 2109, Australia by 30 September 2001. Applications will not be acknowledged unless specifically requested. Women are particularly encouraged to apply. Equal Employment Opportunity and No Smoking in the Workplace are University Policies. www.jobs.mq.edu.au From rrosebru@mta.ca Thu May 24 21:36:57 2001 -0300 Return-Path: Received: (from Majordom@localhost) by mailserv.mta.ca (8.11.1/8.11.1) id f4ONgLq12088 for categories-list; Thu, 24 May 2001 20:42:21 -0300 (ADT) X-Authentication-Warning: mailserv.mta.ca: Majordom set sender to cat-dist@mta.ca using -f From: "regivan" To: Subject: categories: Intervals as a Model of Real Type Date: Thu, 24 May 2001 10:13:27 -0300 Message-ID: MIME-Version: 1.0 Content-Type: text/plain; charset="iso-8859-1" X-Priority: 3 (Normal) X-MSMail-Priority: Normal X-Mailer: Microsoft Outlook IMO, Build 9.0.2416 (9.0.2910.0) Importance: Normal X-MimeOLE: Produced By Microsoft MimeOLE V5.00.2314.1300 X-MIME-Autoconverted: from 8bit to quoted-printable by imap.ufrn.br id KAA09256 Content-Transfer-Encoding: 8bit X-MIME-Autoconverted: from quoted-printable to 8bit by mailserv.mta.ca id f4ODD3b08040 Sender: cat-dist@mta.ca Precedence: bulk Status: O X-Status: X-Keywords: X-UID: 42 What are the desired properties for a model of real type? 1) It must be a field or work like it, etc. I intend to endow intervals with a weak notion of equivalence, what make it works like a field, what will enable us to use intervals an representations of real numbers. What are the desired properties that the resulting structure must satisfy. Some bibliography is welcome. My Best Regards Regivan ------------------------ Prof. Dr. Regivan H. N. Santiago Programa de Mestrado em Sistemas e Computação. Departamento de Informática e Matemática Aplicada - DIMAp Universidade Federal do Rio Grande do Norte - UFRN e-mail: regivan@dimap.ufrn.br From rrosebru@mta.ca Fri May 25 08:23:57 2001 -0300 Return-Path: Received: (from Majordom@localhost) by mailserv.mta.ca (8.11.1/8.11.1) id f4PAaDe11642 for categories-list; Fri, 25 May 2001 07:36:13 -0300 (ADT) X-Authentication-Warning: mailserv.mta.ca: Majordom set sender to cat-dist@mta.ca using -f From: Jiri Adamek Message-Id: <200105251034.MAA03907@lisa.iti.cs.tu-bs.de> Subject: categories: connected functors and pseudoepis To: categories@mta.ca Date: Fri, 25 May 2001 12:34:04 +0200 (MET DST) X-Mailer: ELM [version 2.5 PL2] MIME-Version: 1.0 Content-Type: text/plain; charset=us-ascii Content-Transfer-Encoding: 7bit Sender: cat-dist@mta.ca Precedence: bulk Status: O X-Status: X-Keywords: X-UID: 43 The connected functors we have mentioned the other day, i.e. those functors p: E -> B for which (-).p Set^B -> Set^E is fully faithful, are easily seen to be precisely the lax epimorphisms of the 2-category Cat (of small categories). We do not know whether every pseudoepimorphism in Cat is connected, does anyone know? The answer is affirmative if B is a preorder. J.Adamek, R. El Bashir, M. Sobral and J. Velebil xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx alternative e-mail address (in case reply key does not work): J.Adamek@tu-bs.de xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx From rrosebru@mta.ca Sat May 26 02:43:56 2001 -0300 Return-Path: Received: (from Majordom@localhost) by mailserv.mta.ca (8.11.1/8.11.1) id f4Q52UI18176 for categories-list; Sat, 26 May 2001 02:02:30 -0300 (ADT) X-Authentication-Warning: mailserv.mta.ca: Majordom set sender to cat-dist@mta.ca using -f From: fribourg@lsv.ens-cachan.fr Date: Fri, 25 May 2001 16:24:16 +0200 Message-Id: <200105251424.QAA18603@quetsche.lsv.ens-cachan.fr> To: csl01-list@lsv.ens-cachan.fr Subject: categories: CSL 2001 -- CALL FOR PARTICIPATION MIME-Version: 1.0 Content-Type: text/plain; charset=iso-8859-1 X-MIME-Autoconverted: from 8bit to quoted-printable by ariane.ens-cachan.fr id f4PEOgUN029649 Content-Transfer-Encoding: 8bit X-MIME-Autoconverted: from quoted-printable to 8bit by mailserv.mta.ca id f4PERqb05604 Sender: cat-dist@mta.ca Precedence: bulk Status: RO X-Status: X-Keywords: X-UID: 44 CSL 2001 September 10 - 13, 2001 Paris, France Annual Conference of the European Association for Computer Science Logic ------------------------------------------------------------ EARLY REGISTRATION IS NOW OPEN! DEADLINE: JUNE 25 ------------------------------------------------------------ The CSL Web page contained a detailed schedule and registration form http://www.lsv.ens-cachan.fr/csl01/ Invited talks: ************** Jean-Yves Girard (IML, Marseille) Peter O'Hearn (QMW College, London) Jan Van den Bussche (U. Limburg) Contributed papers: ****************** M. Galota and H. Vollmera: ``Generalization of the Buechi-Elgot-Trakhtenbrot Theorem''. T.M. Rasmussen: ``Labelled Natural Deduction for Interval Logics''. M. Schmidt-Schauss: ``Stratified Context Unification is in PSPACE''. O. Finkel: ``An effective extension of the Wagner hierarchy to blind counter automata''. P. Courtieu: ``Normalized types''. Y. Chen and E. Shen: ``Capture Complexity by Partition''. C. Lutz, U. Sattler and F. Wolter: ``Modal Logic and the two-variable fragment''. M. Grohe and S. Wöhrle: ``An Existential Locality Theorem''. F. Koriche: ``A Logic for Approximate First-Order Reasoning''. M. Bezem: ``An improved extensionality criterion for higher-order logic programs''. Y. Akama: ``Limiting Partial Combinatory Algebras Towards Infinitary Lambda-calculi and Classical Logic''. S. Ronchi Della Rocca and L. Roversi: ``Intersection Logic''. A. Armando, S. Ranise and M. Rusinowitch: ``Uniform Derivation of Decision Procedures by Superposition''. F. Klaedtke: ``Decision Procedure for an Extension of WS1S''. P. Chrzastowski-Wachtel, P. Pokarowski and J. Tyszkiewicz: ``On the Existence of Asymptotic Conditional Probabilities in First Order Logic of Word Structures''. M. Keye: ``A principle of induction''. V. Mogbil: ``Quadratic correctness criterion for Non commutative Logic''. J. Power and K. Tourlas: ``An Algebraic Foundation for Higraphs''. R. Staerk and S. Nanchen: ``A Logic for Abstract State Machines''. A. Dawar, E. Grädel and S. Kreutzer: ``Inflationary Fixed Points in Modal Logic''. A. Guglielmi and L. Strassburger: ``Non-Commutativity and MELL in the Calculus of Structures''. M. Korovina and O. Kudinov. ``Semantic Characterisations of Second-order Computability Over the Real Numbers''. E. Robinson and G. Rosolini: ``An Abstract Look at Realizability''. N. Alechina, M. Mendler, V. de Paiva and E. Ritter: ``Categorical and Kripke Semantics for Constructive Modal Logics''. L. Schroeder: ``Life without the terminal type''. J. van Eijck: ``Constrained Hyper Tableaux'' F. S. de Boer and R. M. van Eijk: ``Decidable Navigation Logics for Object Structures''. W. Charatonik and J.-M. Talbot: ``The Decidability of Model Checking Mobile Ambients''. J.-Y. Marion: ``Actual arithmetic and feasibility''. N. Schweikardt: ``The natural order-generic collapse for omega-representable databases over the rational andthe real ordered group''. M. Baaz and G. Moser: ``On a generalisation of Herbrand's Theorem''. M. Kanovich. ``The Expressive Power of Horn Monadic Linear Logic''. V. Danos and R. Harmer: ``The Anatomy of Innocence''. A. Kopylov and A. Nogin. ``Markov's Principle for Propositional Type Theory''. C. Schuermann ``Recursion for Higher-Order Encodings''. R. Matthes: ``Monotone Inductive and Coinductive Constructors of Rank 2''. G. Rosu: ``Complete Categorical Equational Deduction''. S. Abramsky and M. Lenisa: ``A Fully Complete Minimal PER Model for the Simply Typed lambda-calculus''. J. Goubault-Larrecq: ``Well-Founded Recursive Relations''. H. Ohsaki: ``Beyond the Regularity: Equational Tree Automata for Associative and Commutative Theories''. -- Laurent Fribourg Tel. +33 1 47 40 28 66 From rrosebru@mta.ca Mon May 28 00:03:42 2001 -0300 Return-Path: Received: (from Majordom@localhost) by mailserv.mta.ca (8.11.1/8.11.1) id f4S2Sx405555 for categories-list; Sun, 27 May 2001 23:28:59 -0300 (ADT) X-Authentication-Warning: mailserv.mta.ca: Majordom set sender to cat-dist@mta.ca using -f Date: Sat, 26 May 2001 12:22:37 +0200 Message-Id: <200105261022.MAA32435@tosca.dmi.unict.it> From: Vladimiro Sassone To: categories@mta.ca Subject: categories: Concoord 2001: Call for Participation Sender: cat-dist@mta.ca Precedence: bulk Status: RO X-Status: X-Keywords: X-UID: 45 [[ -- Apologies for multiple copies of this message -- \vs ]] Final Call for Participation ConCoord International Workshop on Concurrency and Coordination ====================================================== Scientific Programme Fri July 6 09:00- 9:30 Registration and Opening 09:30-10:30 Invited Talk: `A Query Language Based on the Ambient Logic' Luca Cardelli 10:30-11:00 Coffee Break 11:00-11:45 `Coordination of Mobile Components', F. Arbab 11:45-12:30 `CoreLime: a Coordination Model for Mobile Agents', B. Carbunar, M.T. Valente, J. Vitek 12:30-14:30 Lunch 14:30-15:15 `Network Services and Modal Types', G. Ferrari, E. Moggi, R. Pugliese 15:15-16:00 `Boxed Ambients: Types and Security', M. Bugliesi, G. Castagna, S. Crafa 16:00-16:30 Coffee Break 16:30-18:00 PANEL: Concurrency, Coordination, and Global Computing Sat Jul 7th 09:00-10:00 Invited Talk: Jim Waldo (title TBA) 10:00-10:30 Coffee Break 10:30-11:15 `Security Issues in Component-based Design', A. Bracciali, A. Brogi, G. Ferrari, E. Tuosto 11:15-12:00 `Information Flow Security in Mobile Ambients', A. Cortesi, R. Focardi 12:00-12:45 `Static Analysis for Stack Inspection', M. Bartoletti, P. Degano, G. Ferrari Sun Jul 8th 09:00-10:00 Invited Talk: Paolo Ciancarini (title TBA) 10:00-10:30 Coffee Break 10:30-11:15 `Modelling Node Connectivity in Dynamically Evolving Networks', L. Bettini, M. Loreti, R. Pugliese 11:15-12:00 `On the Serializability of Transactions in JavaSpaces' N. Busi, G. Zavattaro 12:00-12:45 `Zero-safe net models for transactions in Linda', R. Bruni and U. Montanari --------------------------------------------------------------------------- Travel Lipari is the largest island of the Eolie Archipelago, located north of Sicily, well known for its volcanic activities. It has sceneries of incomparable beauty and contrasting character. It can be easily reached from Milazzo, Palermo, Naples, Messina and Reggio Calabria by ferry or hydrofoil (50 minutes from Milazzo). The suggested route is to fly to Catania (CTA), reach the port of Milazzo by bus, and from there reach Lipary by hydrofoil or ferry. Alternatively, fly to Reggio Calabria (REG) and the Lipari by hydrofoil. Detailed instructions and timetables will be emailed to the participants at registration. --------------------------------------------------------------------------- Costs The workshop registration fee is 220K ITL (around 110 euro), payable cash at the meeting. A social dinner will be organised on Fri Jul 6. Participants will be able to join the excursion to the volcano Stromboli planned for Sun 8 for the Lipari School. --------------------------------------------------------------------------- Registration and Hotel Reservation Due to the high season in Lipari, hotels may be expensive and booking may be difficult. The organisation has (a limited number of) rooms available for the workshop period at: Hotel Casajanca Tel. +39-090-9880222 Fax +39-090-9813003 (around 70 euros, half board) Hotel Filadelfia 2 Tel. +39-090-9812795, Fax +39-090-9812486 (around 70 euros, half board) Hotel Carasco Tel: +39-090-9811605 Fax +39-090-9811828 (around 110 euros, half board) These will of course be allocated on a first-come-fist-served basis. Casajanca is a pretty, little hotel in a splendid location 3km away from the Hotel Filadelfia , where the workshop takes place. The best way to travel from Casajanca is by scooter. For those who require it, renting a scooter will be organised by the hotel staff. If you wish to stay there, but do not intend to ride a scooter, the hotel will organise minibus rides to the workshop location. When booking, remember to mention Concoord/Lipari School. Other suggested five-star, centrally-located (and substantially more priced) hotels are: Hotel Villa Meligunis Hotel Giardino sul Mare Hotel Rocce Azzurre Finally, the travel agency Longo Travel Tel. +39-090-9880640, Fax. +39 090-9812793, e-mail: longotravel@netnet.it Contact person: Mr. Bartolo rents self catering flats on a weekly basis. Further information about hotels can be found at . To register send an email to with your name, affiliation, dates of arrival and departure, and the hotel you have booked in. (Please, notice that you have to book yourself.) --------------------------------------------------------------------------- More information to appear on: =========================================================================== email: From rrosebru@mta.ca Tue May 29 04:11:45 2001 -0300 Return-Path: Received: (from Majordom@localhost) by mailserv.mta.ca (8.11.1/8.11.1) id f4T6W0j15077 for categories-list; Tue, 29 May 2001 03:32:00 -0300 (ADT) X-Authentication-Warning: mailserv.mta.ca: Majordom set sender to cat-dist@mta.ca using -f From: Steve Stevenson MIME-Version: 1.0 Content-Type: text/plain; charset=us-ascii Content-Transfer-Encoding: 7bit Message-ID: <15122.20654.237932.569778@merlin.cs.clemson.edu> Date: Mon, 28 May 2001 09:20:46 -0400 (EDT) To: categories@mta.ca Subject: categories: Theory of computing text as categories X-Mailer: VM 6.72 under 21.1 (patch 11) "Carlsbad Caverns" XEmacs Lucid Sender: cat-dist@mta.ca Precedence: bulk Status: O X-Status: X-Keywords: X-UID: 46 Good morning, Does anyone have a bibliography of typical "computer science" version of computability from the strict category view? I am thinking of texts that are along the lines Hopcroft and Ullman's "Automata, Languages, and Computation". MathRev lists about 80 entries satisfying "computability" and "category theory" but I don't see any textbooks in the mix. Any help appreciated. steve From rrosebru@mta.ca Tue May 29 04:12:02 2001 -0300 Return-Path: Received: (from Majordom@localhost) by mailserv.mta.ca (8.11.1/8.11.1) id f4T6jlW08526 for categories-list; Tue, 29 May 2001 03:45:47 -0300 (ADT) X-Authentication-Warning: mailserv.mta.ca: Majordom set sender to cat-dist@mta.ca using -f Date: Mon, 28 May 2001 16:35:17 -0400 (EDT) From: Peter Freyd Message-Id: <200105282035.f4SKZHA03728@saul.cis.upenn.edu> To: categories@mta.ca Subject: categories: Journal boycott Sender: cat-dist@mta.ca Precedence: bulk Status: RO X-Status: X-Keywords: X-UID: 47 [Note from moderator: The article Peter forwards mentions the Public Library of Science whose web site is at http://www.publiclibraryofscience.org/ where support is being sought.] Science world in revolt at power of the journal owners James Meek, science correspondent Guardian Saturday May 26, 2001 Scientists around the world are in revolt against moves by a powerful group of private corporations to lock decades of publicly funded western scientific research into expensive, subscription-only electronic databases. At stake in the dispute is nothing less than control over the fruits of scientific discovery - millions of pages of scientific information which may hold the secrets of a cure for Aids, cheap space travel or the workings of the human mind. More than 800 British researchers have joined 22,000 others from 161 countries in a campaign to boycott publishers of scientific journals who refuse to make research papers freely available on the internet after six months. "Science depends on knowledge and technology being in the public domain," said Michael Ashburner, professor of biology at Cambridge University and one of the leading British signatories of the campaign, the Public Library of Science (PLS). "In that sense, science belongs to the people, and the fruits of science shouldn't be owned or even transferred by publishers for huge profits. The fruits of our research - which is, overwhelmingly, publicly paid for - should be made available as widely and as economically as possible." Anger has been simmering for more than a decade in the research libraries of Europe and the US at the massive increase in the cost of subscriptions to scientific journals, which collectively make up the sum of the world's scientific research. As the power of the internet to mine electronically archived journals for data grows, scientists have become increasingly frustrated at the journal publishers' plans to keep tight, lucrative control over decades of their work. Last year the most powerful journal publisher, the Anglo-Dutch firm Reed Elsevier, made a profit of #252m on a turnover of #693m in its science and medical business. Elsevier Science and other journal publishers effectively benefit from the public purse twice: once when taxpayer-funded scientists submit their work to the journals for free, and again when taxpayer-funded libraries buy the information back from them in the form of subscriptions. In Britain, the government is so concerned about the power of Reed Elsevier that it has blocked its #3.2bn takeover of another big journal publisher, Harcourt, while complaints about its market dominance are investigated. Derk Haank, the head of Elsevier Science, protested at the singling out of his company, and portrayed the boycott group as naive idealists. "Everybody would like to have everything available, all the time, and preferably for free," he said. "That's a general human trait, but I'm not sure the business model is realistic. I'm not ashamed to make a profit. I would only be ashamed if people were saying I was delivering a lousy service." He added: "Research is publicly funded, but the cost of publishing it isn't. If the funding authorities were to decide to pay for publication I would provide it for free." You won't find copies of most of Reed Elsevier's 1,100 journals on newsagents' shelves. With titles like Thin Walled Structures, Urban Water, Journal of Supercritical Fluids and Trends in Parasitology, their publications don't have the allure of Elle or FHM but the price of a year's subscription would make mass market publishers drool with envy. A year's subscription to Alcohol - nine issues - comes in at about #100 an issue. One Elsevier journal, Brain Research, costs more than #9,000 a year. Another, Preventative Veterinary Medicine, is now #713 a year, an increase of more than 300% over its 1991 price of #171. Elsevier justifies the increases on the grounds that the number of articles being submitted increases each year, adding to the firm's costs. Each article must be peer-reviewed by fellow scientists to see if it is worthy of publication. Mr Haank added that his firm's price increases forced libraries to cut subscriptions, which in turn cut Elsevier's income, forcing them to increase prices still more. Elsevier wanted to get out of this vicious circle, he said, and was trying to get universities to sign up for electronically archived versions of its journals. The firm has taken on 1,500 people to put its entire journal archive - going back to 19th century editions of The Lancet - on computer databases. But he said the price of subscription to the electronic database would still be tightly linked to the ever rising cost of the paper journals. "Our plan is to make everything available in the academic or professional environment, not just in six months, but on day one," he said. "Somebody has to pay for the cost of the system." Scientific research is not considered real unless it has been published in a recognised journal, and scientists' status and promotion is tied to publication. As a rule, neither the scientists who write the papers, nor their colleagues who peer review them, nor the editorial boards who vet them, are paid. The publishers' costs are printing, the tiny full-time staff on each journal - typically two people - marketing, and distribution. While the feud over the price of journals was between libraries and publishers, the scientists stood aside, but the advent of the internet has changed everything. Powerful search engines trawling computer databases make it possible for scientists to discover groundbreaking links between different research results which would previously have taken years of trawling through a jungle of indexes. The prospect of this incredible new tool being controlled by large private corporations has jerked scientists into action. "The major commercial publishers have every reason to feel threatened," Prof Ashburner said. "They charge very high prices, and they are very insistent on copyright transfer. We are not paid for publication, and we see no reason whatsoever why we should hand over copyright to a commercial publisher, having done the work, both the science and the writing. "The costs these publishers are charg ing are such that even in the wealthy countries we can't always afford to buy the information back, and it's off-limits totally for the developing world." In a letter to the competition commission in March, Clive Field, librarian at Birmingham University and head of the Consortium of University Research Libraries said that the Elsevier-Harcourt merger would give one company control over journals representing 42% of a typical university's spend in that area. He said Elsevier and Harcourt were already trying to drive too tough a deal with their electronic archive. "Neither publisher has yet offered a deal which is recognised to be fair and equitable," he wrote. "It is not unnaturally feared that a merged publisher, operating in a market where the buyer is weak, would be even less subject to the price checks and balances that a more open market would offer." A nice little earner Title Brain Research Publisher Elsevier Annual subscription 1991 #3,713 Annual subscription 2001 #9,148 Increase 146% Title Journal of Virological Methods Publisher Elsevier Subscription 1991 #527 Subscription 2001 #1,555 Increase 195% Title Neuroscience Letters Publisher Elsevier Subscription 1991 #1,125 Subscription 2001 #2,805 Increase 149% Title Preventative Veterinary Medicine Publisher Elsevier Subscription 1991 #171 Subscription 2001 #713 Increase 317% Title Biochemical Journal Publisher Biochemical Society (not-for-profit body) Subscription 1991 #793 Subscription 2001 #1,334 Increase 68% Source: Consortium of University Research Libraries From rrosebru@mta.ca Wed May 30 00:24:37 2001 -0300 Return-Path: Received: (from Majordom@localhost) by mailserv.mta.ca (8.11.1/8.11.1) id f4U302p29954 for categories-list; Wed, 30 May 2001 00:00:02 -0300 (ADT) X-Authentication-Warning: mailserv.mta.ca: Majordom set sender to cat-dist@mta.ca using -f Date: Tue, 29 May 2001 23:42:31 -0300 (ADT) From: Bob Rosebrugh To: categories@mta.ca Subject: categories: Re: journal boycott Message-ID: MIME-Version: 1.0 Content-Type: TEXT/PLAIN; charset=US-ASCII Sender: cat-dist@mta.ca Precedence: bulk Status: O X-Status: X-Keywords: X-UID: 48 [Note from moderator: Michael Barr suggested that his contribution to the Newsletter on Serials Pricing be circulated.] ISSN: 1046-3410 NEWSLETTER ON SERIALS PRICING ISSUES NO 229 - July 13, 1999 Editor: Marcia Tuttle CONTENTS 229.1 WHERE DOES THE MONEY GO? Michael Barr 229.1 WHERE DOES THE MONEY GO? Michael Barr, Department of Mathematics and Statistics, McGill University, barr@barrs.org I have been reading the prices newsletter for a year and a half and I would like to make some comments, especially to refute some of the more outrageous claims made by publishers. I believe that I have an unusually broad perspective on the publishing business, having witnessed it from several angles. First and foremost, I have been an active researcher (in mathematics), having been author (or occasionally coauthor) of some 70 articles and coauthor of two books, one of which is about to go into its third edition. Second, I have been member and chair of the Canadian Mathematical Society (CMS) publications committee and have a clear idea of what its publishing costs actually are. Third, I am an editor or associate editor of two print journals, one published by a commercial publisher and one by a university press, as well as editor of two electronic journals, both distributed free. Finally, my daughter worked for two years around 1990 in the journals department of an academic publisher and I have had extensive discussions with her about her experiences and those of people she knows who are still in the field. The CMS journals are not the cheapest journals published by a society but still beat any commercial journal by a factor of 2 to 5, according to the figures collected by Ron Kirby. There used to be page charges, but only about 30% of the authors paid them and they were eventually abandoned as more trouble than they were worth. Despite this, the CMS has a clear profit of perhaps $100,000/year, and this is a major source of income for the society (which has maybe 1000 members). This is real, not paper profit. What expenses do we skip by not being commercial? We have some typesetting costs but most of the articles now come already set in the mathematical typesetting system TeX that has rapidly become the standard for mathematical publication. But this is also true for the commercial journals. As a result, publishing costs have dropped substantially in recent years, although not as much as we were led to believe. Incidentally, twenty and thirty years ago, publishers claimed that the reason mathematics was so expensive to publish was the typesetting costs. Now that most manuscripts come in already typeset, they claim that typesetting was a negligible part of the cost. We have to pay for copy editing costs, printing, binding, mailing, etc. We do little advertising, but advertising is not a major item for established journals in any case. Once upon a time we got free office space, telephone and mailing privileges and even some secretarial services from the university where the editors were, but as university budgets have tightened, we have had to start paying for these just like any commercial journal. The one expense we clearly do not have is a stipend paid the editor-in- chief. I do not know how much that is, but it cannot be significant for a journal that costs $3000 a year and has a subscription base of 1000. So where does all the money go? One answer was supplied by my daughter who informs me that her publisher had five levels of administrators who had no day-to-day contact with the actual publishing, but make decisions increasingly removed from reality and draw six or even seven figure salaries. No doubt, the higher executives travel first class, or perhaps by corporate jet. By contrast, the CMS journals are overseen by a publication committee, the executive committee and board of directors of the society and, ultimately, the membership, all of whom exercise a very light hand and operate gratis. Of course, if societies were to undertake to publish dozens of journals, this structure would no longer work. So one answer is surely that in academic journal publishing, there are few, if any, economies of scale and very serious diseconomies. In that case, the fact that publishing is falling into fewer and fewer hands is even more disturbing. The electronic journal I help edit, _Theory and Applications of Categories_, is free and available to everyone with an internet connection. We have published only about a dozen papers a year, but that's ok; we want to establish a reputation and have it there if the other journals fold. I have announced publicly that I will neither referee for nor submit papers to high priced commercial journals. I quite recently refused to become an editor for a new journal that was to have been published by, I think, Birkhaeuser. Partly for that reason, the to-be editor decided to make it electronic instead. I should add that not all commercial publishers are high priced. There are a couple of small publishers that are publishing good journals at reasonable prices. As an author, I am beginning to feel ill-used. I spend the time doing the research, writing it up and so on and the journals end up owning it. The quid pro quo is forty or fifty "free" reprints? They tell us that copyright acts are there to protect intellectual property, but they certainly don't protect mine. My interests are served by distribution as wide as possible and the publishers' by restricting distribution to the few that can still pay for it. For the last two papers published in a commercial journal, I altered the copyright form to retain the right to post electronically. The publisher accepted it, but would they if a large number of authors did it? I do know that one colleague of mine got a letter from a publisher's lawyer ordering him to remove one of his papers from his electronic archive. Actually, it is only in the last 15 or 20 years that I have been even asked to sign copyright documents; perhaps since the 1976 US copyright act. Before that, the issue never arose. The CMS journals and the electronic journal I edit ask only for a one-time licence. When you ask what a publisher adds to a publication, there is copy editing, printing, binding, mailing, subscription servicing and maybe a tiny bit of publicity (once the journal is established). I think they also add an enormous amount of often useless overhead. When published electronically, only the copy-editing remains. Since our journal is published free, this is not done in any systematic way. It is left to the author and I, on one occasion, returned a paper to the author for serious TeX deficiencies. He had to hire someone to repair it since he refused to learn enough TeX to do it himself. That is unfortunate and I sympathize with him, but think of it as a form of page charge. As an editor, I do for free exactly what I do for the other two journals for free. The editor-in-chief (actually called managing editor) of the electronic journal does more. He spends 3-6 hours on each paper and, so long as we have only a dozen a year, he does not mind. But he and the other editors are aware that there is a serious problem brewing here and we do not know what to do about it. The obvious thing would be for the universities to take some part of their serials budget and simply subsidize these activities that have the potential of enormous savings in the long run. But how do you get there from here? Although this would sap the library's budget, it should not result in loss of jobs in the library since exactly the same (or more) tasks of storage, archival and retrieval would exist. It would only sap the journal acquisitions budget. But what I don't see is how the universities could be made to share these costs in an equitable fashion. Some would subsidize these electronic journals and others would be tempted to sponge off those. This is a problem, but not I think an insuperable one. Why do we publish in journals at all? In fact, all my papers in the last ten years have been distributed electronically and are old hat by the time they are published. We all know the answer. For promotions and tenure (no longer an issue for me) and research grants (I still have a good one and would like to keep it). Thus the only real problem is that of certification. And acceptance of electronic publication is growing. Note that we did not name our journal "Electronic journal .." We decided it would be like naming it "The A4 journal of.." In the end, I think there will be good and poor electronic journals just as there are good and poor print journals. For the time being, however, I am not recommending electronic publication for young researchers. A recent writer to this newsletter made the fatuous suggestion that free electronic journals might be violating the anti-trust laws. An elephant cannot sue a mouse for anti-trust violations. The anti- trust laws are not there to guarantee a business success; they are there to protect consumers from price gouging by a monopolist. If an airline is sued over low prices, it is not the low prices that are the ultimate problem but the likelihood that, once the competitor is driven out of the market, the price will be raised to a much higher level. The history of People's Air shows that this is not just a theory. Much as I would like to see some of the commercial publishers driven out of business, I know this is not likely to happen. Even if did, the publishers of electronic journals could not raise prices the way paper journals have since the barriers to starting new ones are so low. Since anti-trust was mentioned, it is a wonder to me that some state attorneys-general haven't decided that the journals are running a monopolistic business and are engaged in price gouging. After all, a significant part of the state universities' budgets are going to these publishers. The fact that, as recently pointed out in these pages, a few private universities can still afford these journals is irrelevant. But let us engage in some speculation by supposing that it is illegal to do work gratis. Then the most guilty are the researchers who do the work in the first place and give it away to the publishers. Perhaps the publishers ought to be required to pay serious money for the rights to publish. It was one thing when the major journals were non-profit and were performing a service to the profession just by existing. But now it is a big business; why should they not pay for their raw materials. Then there is the free editorial work. I believe the editors-in-chief do get a significant "honorarium." But the remaining editors do not usually get so much as a postage stamp. At least, I never have. The authors and editors at least get some recognition for their work. What about the anonymous referees? Honest refereeing is hard work and there is no payoff, either in money or honor. Yet without it the whole system would come crashing down. It was done free for the good of the profession in the old days, since the journals themselves were non- profit. When commercial journals came along (which started, at least in a big way, in the 1960s), we just went along with free refereeing since, it was what we were accustomed to. What would have happened if the referees had insisted on being paid? I, for one, have just made a personal decision to do no more unpaid refereeing for commercially published journals. No decision I have ever made in my professional career has been less painful. If more of us adopted such a policy, the whole enterprise would collapse. Moreover, it would cost us individually nothing since only the editors would know. As an editor, I will still ask people to referee papers, but if they all refuse, the journal will disappear. One new feature on the publishing scene is that several of the old line journals that used to be published by mathematical societies, especially in Europe, have been taken over by commercial houses. I assume that the societies sell them for a tidy sum. The price usually stays low for a few years and then starts rising often to stratospheric heights. My department is likely to stop subscribing to the oldest mathematical journal in the world, of which we have a complete set. It will be a painful decision, but the journal is very expensive and no longer of much importance. I have not mentioned the actual disparity of costs. I recently calculated the cost per page, for each of the nearly one hundred journals we had a paid subscription to in 1996 (we also have a substantial number of exchange subscriptions, all non-commercial). I realize that this is a crude measure, since not all pages are the same size. But at least it is better than just looking at subscription cost. The costs per page ranged from $.04 to $4.86. If you remove the top and bottom ten, the range is $.18 to $1.37, a factor of over 7. The journal at $.18 happens to be on anybody's list of the top 5 mathematics journals in the world. So does the eighth most expensive, which costs $1.51. There is no correlation between price and quality. There was one commercial journal at $.38 and one society published journal at $.75 and they were the respective extremes. But every journal that cost more than $.75 (a couple of Russian translations excepted) was commercially published and everyone below $.38 was published by a society or a university. The figures show that some of the top journals in the world are among the cheapest. Unfortunately, a couple of the top journals are among the most expensive and this will be our most difficult decision as we have to cut about 10% from our budget, while prices are estimated to rise 13% besides (part of that due to exchange rate fluctuations). +++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++ Statements of fact and opinion appearing in the _Newsletter on Serials Pricing Issues_ are made on the responsibility of the authors alone, and do not imply the endorsement of the editor, the editorial board, or the University of North Carolina at Chapel Hill. +++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++ Readers of the _Newsletter on Serials Pricing Issues_ are encouraged to share the information in the newsletter by electronic or paper methods. We would appreciate credit if you quote from the newsletter. +++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++ The _Newsletter on Serials Pricing Issues_ (ISSN: 1046-3410) is published by the editor through Academic Technology and Networks at the University of North Carolina at Chapel Hill, as news is available. Editor: Marcia Tuttle, Internet: marcia_tuttle@unc.edu; Telephone: 919 929-3513. Editorial Board: Keith Courtney (Taylor and Francis), Fred Friend (University College London), Birdie MacLennan (University of Vermont), Michael Markwith (Swets Subscription Services), James Mouw (University of Chicago), Heather Steele (Blackwell's Periodicals Division), David Stern (Yale University), and Scott Wicks (Cornell University). To subscribe to the newsletter send a message to LISTPROC@UNC.EDU saying SUBSCRIBE PRICES [YOUR NAME]. Be sure to send that message to the listserver and not to Prices. You must include your name. To unsubscribe (no name required in message), you must send the message from the e-mail address by which you are subscribed. If you have problems, please contact the editor. Back issues of the Newsletter are archived on two World Wide Web sites. At UNC-CH the url is: http://www.lib.unc.edu/prices/. At Grenoble the url is: http://www-mathdoc.ujf- grenoble.fr/NSPI/NSPI.html. +++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++ From rrosebru@mta.ca Wed May 30 00:27:21 2001 -0300 Return-Path: Received: (from Majordom@localhost) by mailserv.mta.ca (8.11.1/8.11.1) id f4U38K023626 for categories-list; Wed, 30 May 2001 00:08:20 -0300 (ADT) X-Authentication-Warning: mailserv.mta.ca: Majordom set sender to cat-dist@mta.ca using -f X-Originating-IP: [198.168.181.116] From: "Marta Bunge" To: categories@mta.ca Subject: categories: preprint: Constructive Galois Toposes /email address Date: Tue, 29 May 2001 20:22:25 -0400 Mime-Version: 1.0 Content-Type: text/plain; format=flowed Message-ID: X-OriginalArrivalTime: 30 May 2001 00:22:25.0707 (UTC) FILETIME=[9A4517B0:01C0E89E] Sender: cat-dist@mta.ca Precedence: bulk Status: O X-Status: X-Keywords: X-UID: 49 The paper Marta Bunge & Eduardo Dubuc, "Constructive Theory of Galois Toposes" has just been posted in my homepage http://www.math.mcgill.ca/~bunge/current_papers.html/ctgt.ps (dvi) I would also appreciate any communication with me to be through my hotmail address during the next seven months. I shall be visiting Ross Street in Sydney until the end of December 2001. Thank you. Best regards, Marta Bunge E-mail: martabunge@hotmail.com From rrosebru@mta.ca Thu May 31 07:13:32 2001 -0300 Return-Path: Received: (from Majordom@localhost) by mailserv.mta.ca (8.11.1/8.11.1) id f4V9X4X26945 for categories-list; Thu, 31 May 2001 06:33:04 -0300 (ADT) X-Authentication-Warning: mailserv.mta.ca: Majordom set sender to cat-dist@mta.ca using -f X-Originating-IP: [198.168.182.19] From: "Marta Bunge" To: categories@mta.ca Subject: categories: correction Date: Wed, 30 May 2001 11:01:36 -0400 Mime-Version: 1.0 Content-Type: text/plain; format=flowed Message-ID: X-OriginalArrivalTime: 30 May 2001 15:01:36.0574 (UTC) FILETIME=[6C3C9DE0:01C0E919] Sender: cat-dist@mta.ca Precedence: bulk Status: RO X-Status: X-Keywords: X-UID: 51 To access the paper "Constructive Theory of Galois Toposes" go to http://www.math.mcgill.ca/~bunge/ctgt.ps (.pdf) as the one I gave earlier does not work. Sorry! Marta Bunge _________________________________________________________________________ Get Your Private, Free E-mail from MSN Hotmail at http://www.hotmail.com. From rrosebru@mta.ca Thu May 31 07:14:04 2001 -0300 Return-Path: Received: (from Majordom@localhost) by mailserv.mta.ca (8.11.1/8.11.1) id f4V9VQI15400 for categories-list; Thu, 31 May 2001 06:31:26 -0300 (ADT) X-Authentication-Warning: mailserv.mta.ca: Majordom set sender to cat-dist@mta.ca using -f Date: Tue, 29 May 2001 21:38:43 -0700 (PDT) From: Bill Rowan Message-Id: <200105300438.f4U4chS51110@transbay.net> To: categories@mta.ca Subject: categories: Pro C Sender: cat-dist@mta.ca Precedence: bulk Status: RO X-Status: X-Keywords: X-UID: 52 I have read that if C is a category, and the axiom of choice is assumed, then Pro C is equivalent to its full subcategory of diagrams where the diagram category is an inversely-directed set. Does anyone know where this is proved in the literature? Thanks, Bill Rowan From rrosebru@mta.ca Thu May 31 21:34:49 2001 -0300 Return-Path: Received: (from Majordom@localhost) by mailserv.mta.ca (8.11.1/8.11.1) id f5109cV27825 for categories-list; Thu, 31 May 2001 21:09:38 -0300 (ADT) X-Authentication-Warning: mailserv.mta.ca: Majordom set sender to cat-dist@mta.ca using -f To: categories@mta.ca, rrosebrugh@mta.ca Subject: categories: Re: journal boycott Message-Id: From: Paul Taylor Date: Wed, 30 May 2001 16:58:50 +0100 X-Ident: pt Sender: cat-dist@mta.ca Precedence: bulk Status: RO X-Status: X-Keywords: X-UID: 59 I completely agree with the views about commercial journals in - Mike Barr's article in the "Newsletter on serials pricing issues" (29 May), - Peter Johnstone's resignation letter as an editor of JPAA (15 Jan), - James Meek's article ("Guardian", 26 May) on the cost of journals (28 May). (The dates refer to "categories" postings.) As Mike Barr pointed out, but James Meek seems not to know, the journals no longer do the work of typesetting papers, so in the Web age the commercial publishers do NOTHING AT ALL. Without meaning to diminish my agreement that we should stop giving our research and our institutions' money to the commercial publishers, I would like to be "advocatus diaboli" on an issue of management. My question is this: Is a commercial (or university) publisher, being outside the academic community, better able to deal with complaints against editors than an academic managing editor can be? An academic editor is subject to other pressures, which may be summed up as "not falling out with colleagues", whereas a commercial manager can be more ruthless in enforcing the rules. I am thinking of complaints of a management rather than intellectual nature, of course. For example, failing to pass papers from authors to referees and the referees' reports back again within a reasonable time. (This has been a real issue for me, but I have no intention of naming names. I would like to see a discussion of professional standards of editing and refereeing sometime, but not on THIS occasion.) The kind of answer that I'm looking for would be an (anonymised) account of some incident where a commercial publisher has dealt with a complaint better or worse than an academic managing editor would. Paul From rrosebru@mta.ca Thu May 31 21:35:00 2001 -0300 Return-Path: Received: (from Majordom@localhost) by mailserv.mta.ca (8.11.1/8.11.1) id f5104R904108 for categories-list; Thu, 31 May 2001 21:04:27 -0300 (ADT) X-Authentication-Warning: mailserv.mta.ca: Majordom set sender to cat-dist@mta.ca using -f Subject: categories: Re: Journal boycott To: categories@mta.ca Date: Wed, 30 May 2001 15:29:08 +0100 (BST) X-Mailer: ELM [version 2.5 PL3] MIME-Version: 1.0 Content-Type: text/plain; charset=us-ascii Content-Transfer-Encoding: 7bit Message-Id: From: Tom Leinster X-Scanner: exiscan *1556y6-00007q-00*V9APLH2CDy6* http://duncanthrax.net/exiscan/ Sender: cat-dist@mta.ca Precedence: bulk Status: RO X-Status: X-Keywords: X-UID: 60 [Note from moderator: This and one further posting address the issue in the subject heading. The items from Peter Freyd and Michael Barr were posted for information, but the subject is not directly relevant. Please send replies for T. Leinster and P. Taylor directly to them rather than the list.] I'm writing to seek suggestions. I'd very much like to sign the boycott letter mentioned in the article forwarded by Peter Freyd (relevant bits quoted below). More generally, I'd prefer to avoid perpetuating the more exploitative aspects of commercial publication. But I'm not going to sign the letter just yet. This is because it seems that if I commit myself to only publishing in "enlightened" journals then my options will be severely restricted, to the extent that it might harm my future job prospects. Unfortunately, it's a sacrifice I'm not quite willing to make. What I'd like to find is that it is actually possible to publish in respected journals while keeping my papers free to whoever wants them. So my first question is: which journals have enlightened policies? I know about TAC, and I've seen the list (http://front.math.ucdavis.edu/journals) of journals which accept submission direct from the electronic archive (and so, presumably, are happy for the papers they publish to be freely available). What other enlightened publications - especially category-theoretic - are there? Mike Barr's article also mentioned copyright agreements, and I'd be interested to know of other people's experiences with this. Which journals are happy for you to retain copyright of your papers, or for you to modify the agreement so that you at least retain the right to make your own work electronically available? And how exactly do you make these modifications (e.g. wording)? Is it perhaps easier just to sign the agreement but post it electronically anyway, and hope no-one notices? (I would have imagined this perfectly safe except for a certain experience of a colleague.) Well, I'm eager to hear of positive experiences... Thanks, Tom Leinster > Science world in revolt at power of the journal owners [...] > More than 800 British researchers have joined 22,000 others from 161 > countries in a campaign to boycott publishers of scientific journals > who refuse to make research papers freely available on the internet > after six months. [see http://www.publiclibraryofscience.org ] From rrosebru@mta.ca Thu May 31 21:35:58 2001 -0300 Return-Path: Received: (from Majordom@localhost) by mailserv.mta.ca (8.11.1/8.11.1) id f510InV30317 for categories-list; Thu, 31 May 2001 21:18:49 -0300 (ADT) X-Authentication-Warning: mailserv.mta.ca: Majordom set sender to cat-dist@mta.ca using -f Date: Thu, 31 May 2001 13:57:45 +0100 (BST) From: "Dr. P.T. Johnstone" To: categories@mta.ca Subject: categories: Re: Pro C In-Reply-To: <200105300438.f4U4chS51110@transbay.net> Message-ID: MIME-Version: 1.0 Content-Type: TEXT/PLAIN; charset=US-ASCII X-Scanner: exiscan *155S1F-0001Yv-00*ZKzR26atu/k* http://duncanthrax.net/exiscan/ Sender: cat-dist@mta.ca Precedence: bulk Status: O X-Status: X-Keywords: X-UID: 61 On Tue, 29 May 2001, Bill Rowan wrote: > > I have read that if C is a category, and the axiom of choice is assumed, then > Pro C is equivalent to its full subcategory of diagrams where the diagram > category is an inversely-directed set. Does anyone know where this is proved > in the literature? > > Thanks, > > Bill Rowan > Choice isn't needed: all you need is the result that, for any filtered category C, there is a directed poset P and a final functor P --> C. There is a proof of this somewhere in SGA4 (I don't have the reference to hand), where it is attributed to Pierre Deligne; but I suspect it may be older than this. Peter Johnstone From rrosebru@mta.ca Thu May 31 21:36:10 2001 -0300 Return-Path: Received: (from Majordom@localhost) by mailserv.mta.ca (8.11.1/8.11.1) id f510Jgi26995 for categories-list; Thu, 31 May 2001 21:19:42 -0300 (ADT) X-Authentication-Warning: mailserv.mta.ca: Majordom set sender to cat-dist@mta.ca using -f Date: Thu, 31 May 2001 07:42:43 -0400 From: William Boshuck To: categories@mta.ca Subject: categories: Re: Pro C Message-ID: <20010531074243.A26393@triples.math.mcgill.ca> References: <200105300438.f4U4chS51110@transbay.net> Mime-Version: 1.0 Content-Type: text/plain; charset=us-ascii X-Mailer: Mutt 1.0pre3us In-Reply-To: <200105300438.f4U4chS51110@transbay.net> Sender: cat-dist@mta.ca Precedence: bulk Status: O X-Status: X-Keywords: X-UID: 62 This is due to Deligne, and can be found towards the beginning of SGA4, Expose I, section 8. I would like to know of a more recent source that is so (or more) thorough on the subject. cheers, -b On Tue, May 29, 2001 at 09:38:43PM -0700, Bill Rowan wrote: > > I have read that if C is a category, and the axiom of choice is assumed, then > Pro C is equivalent to its full subcategory of diagrams where the diagram > category is an inversely-directed set. Does anyone know where this is proved > in the literature? > > Thanks, > > Bill Rowan From rrosebru@mta.ca Thu May 31 21:43:05 2001 -0300 Return-Path: Received: (from Majordom@localhost) by mailserv.mta.ca (8.11.1/8.11.1) id f510K8v26585 for categories-list; Thu, 31 May 2001 21:20:08 -0300 (ADT) X-Authentication-Warning: mailserv.mta.ca: Majordom set sender to cat-dist@mta.ca using -f From: etaps02@ormelune.imag.fr (Etaps 2002) Date: Thu, 31 May 2001 15:10:48 +0200 (MET DST) Message-Id: <200105311310.PAA04670@pierramenta.imag.fr> Subject: categories: ETAPS 2002, FIRST ANNOUNCEMENT & CALL FOR SUBMISSIONS To: categories@mta.ca Content-Type: text Sender: cat-dist@mta.ca Precedence: bulk Status: RO X-Status: X-Keywords: X-UID: 63 Please apologize if you receive multiple copies of this message. ********************************************************** *** ETAPS 2002 *** *** APRIL, 6-14, 2002 *** *** GRENOBLE, FRANCE *** ********************************************************** The European Joint Conferences on Theory and Practice of Software ETAPS is a loose and open confederation of conferences and other events that has become the primary European forum for academic and industrial researchers working on topics relating to Software Science. ****************************** * http://www-etaps.imag.fr/ * ****************************** FIRST ANNOUNCEMENT & CALL FOR SUBMISSIONS ----------------------------------------------------------------------- 5 Conferences - 13 Satellite Events - Tutorials - Tool Demonstrations ----------------------------------------------------------------------- Conferences ----------------------------------------------------------------------- CC 2001: International Conference on Compiler Construction Chair: Nigel Horspool ESOP 2001, European Symposium On Programming Chair: Daniel Le Metayer FASE 2001, Fundamental Approaches to Software Engineering Chairs: Ralf-Detlef Kutsche and Herbert Weber FOSSACS 2001 Foundations of Software Science and Computation Structures Chair: Mogens Nielsen TACAS 2001, Tools and Algorithms for the Construction and Analysis of Systems Chairs: Perdita Stevens and Joost-Pieter Katoen Satellite Events ----------------------------------------------------------------------- ACL2: Third Workshop on the ACL2 Theorem Prover and its Applications Contact: Matt Kaufmann, matt.kaufmann@amd.com http://www.cs.utexas.edu/users/moore/acl2/workshop-2002/ AGT: APPLIGRAPH Workshop on Applied Graph Transformation Contact: Hans-Jörg Kreowski, kreo@informatik.uni-bremen.de http://www.informatik.uni-bremen.de/theorie/AGT2002 CMCS: Coalgebraic Methods in Computer Science Contact: Larry Moss, University of Indiana, lsm@cs.indiana.edu http://www.cs.indiana.edu/cmcs COCV: Compiler Optimization Meets Compiler Verification Contact: Jens Knoop, knoop@ls5.cs.uni-dortmund.de http://sunshine.cs.uni-dortmund.de/~knoop/cocv02.html DCC: Designing Correct Circuits Contact: Mary Sheeran, ms@cs.chalmers.se http://www.cs.chalmers.se/~ms/DCC02/ INT: Second Workshop on Integration of Specification Techniques for Applications in Engineering Contact: Martin Große-Rhode, mgr@cs.tu-berlin.de http://tfs.cs.tu-berlin.de/~mgr/int02/ LDTA: Second Workshop on Language Descriptions, Tools and Applications Contact: Marjan Mernik, marjan.mernik@uni-mb.si http://www.cwi.nl/conferences/LDTA2002/ SC: Software Composition Contact: Elke Pulvermüller, pulvermueller@acm.org http://i44www.info.uni-karlsruhe.de/~pulvermu/workshops/SC2002 SFEDL: Semantic Foundations of Engineering Design Languages Contact: Gerald Lüttgen, g.luettgen@dcs.shef.ac.uk http://www.dcs.shef.ac.uk/~sfedl SLAP: Synchronous Languages, Applications, and Programming Contact: Florence Maraninchi, Florence.Maraninchi@imag.fr http://www.inrialpes.fr/bip/people/girault/Publications/Slap02 SPIN: 9th International SPIN Workshop on Model Checking of Software Contact: Stefan Leue, spin2002@informatik.uni-freiburg.de http://tele.informatik.uni-freiburg.de/spin2002 TPTS: Theory and Practice of Timed Systems Contact: Oded Maler, Oded.Maler@imag.fr http://www-verimag.imag.fr/~maler/TPTS.html VISS: Validation and Implementation of Scenario-based Specifications Contact: Anca Muscholl, muscholl@liafa.jussieu.fr Tutorials ----------------------------------------------------------------------- Proposals for half-day or full-day tutorials related to ETAPS 2001 are invited. Tutorial proposals will be evaluated on the basis of their assessed benefit for prospective participants to ETAPS 2001. Contact: Saddek Bensalem, Verimag, Saddek.Bensalem@imag.fr Tool Demonstrations ----------------------------------------------------------------------- Demonstrations of tools presenting advances on the state of the art are invited. Submissions in this category should present tools having a clear connection to one of the main ETAPS conferences, possibly complementing a paper submitted separately. Contact: Peter D. Mosses, etaps2002-demo@brics.dk ----------------------------------------------------------------------- INVITED SPEAKERS ----------------------------------------------------------------------- Bruno Courcelle, LaBRI, Bordeaux, France Patrick Cousot, ENS Paris, France John Daniels, Syntropy Limited, London, UK Daniel Jackson, Massachusetts Institute of Technology, USA Michael Lowry, NASA Ames Research Center, USA Greg Morrisett, Cornell University, USA Mary Shaw, Carnegy Mellon University, USA ----------------------------------------------------------------------- IMPORTANT DATES ----------------------------------------------------------------------- October 19, 2001: Submissions Deadline for the Main Conferences, Demos and Tutorials December 14, 2001: Notification of Acceptance/Rejection January 18 2002: Camera-ready Version Due April 8-12, 2002: ETAPS main Conferences in GRENOBLE April 6-14, 2001: Satellite Events ----------------------------------------------------------------------- ----------- you received this e-mail via the individual or collective address categories@mta.ca to unsubscribe from ETAPS list: contact etaps02@ormelune.imag.fr From rrosebru@mta.ca Thu May 31 21:47:09 2001 -0300 Return-Path: Received: (from Majordom@localhost) by mailserv.mta.ca (8.11.1/8.11.1) id f510MKV11251 for categories-list; Thu, 31 May 2001 21:22:20 -0300 (ADT) X-Authentication-Warning: mailserv.mta.ca: Majordom set sender to cat-dist@mta.ca using -f Date: Thu, 31 May 2001 16:11:28 +0200 From: "A. German Puebla Sanchez" Subject: categories: job: Postdoc Positions at the CLIP group To: stacs-mailliste@tcs.inf.tu-dresden.de Reply-to: clip-staff@clip.dia.fi.upm.es Message-id: <200105311411.QAA08369@clip.dia.fi.upm.es> Sender: cat-dist@mta.ca Precedence: bulk Status: RO X-Status: X-Keywords: X-UID: 64 Announcing Postdoc Positions at the CLIP group ---------------------------------------------- School of Computer Science Technical University of Madrid The CLIP (Computational Logic, Implementation and Parallelism) group (http://clip.dia.fi.upm.es) at the School of Computer Science of Technical University of Madrid is searching for candidates for postdoctoral research positions in the research areas in which the group is involved. A PhD in Computer Science or related areas is required. These are research positions (no teaching is compulsory, although it is allowed) and renewable for up to 5 years. The initial salary is 28.548 Euros/year plus an initial budget of 5.707 Euros for travel and other expenses during the first year. Knowledge of Spanish is not a prerequisite for application and candidates can be of any nationality. The working language at the CLIP group for research is English. The number of positions available depends on the quality of the applicants. The positions are co-funded by the Spanish Ministry of Science and Technology and the Technical University of Madrid within the "Ramon y Cajal" program. Interested applicants should send their C.V. and a description of their research interests to the CLIP group (clip-staff@clip.dia.fi.upm.es) by ** June 15 ** Selection will follow a two step process which is described in more detail at http://clip.dia.fi.upm.es/Job_Openings/RyC.html More details on the CLIP group, publications, projects, and research areas of interest can be found at http://clip.dia.fi.upm.es (see e.g. the group description at http://www.clip.dia.fi.upm.es/clip_desc_bysys/clip_desc_bysys.html and the listing of research topics and publications at http://clip.dia.fi.upm.es/clippubsbytopic/clippubsbytopic.html). -- ============================================================= | German Puebla | Facultad de Informatica | | german@fi.upm.es | Universidad Politecnica de Madrid | | Phone +34-91-336-7449 | http://clip.dia.fi.upm.es/~german | ============================================================= From rrosebru@mta.ca Thu May 31 21:47:22 2001 -0300 Return-Path: Received: (from Majordom@localhost) by mailserv.mta.ca (8.11.1/8.11.1) id f510KeL15870 for categories-list; Thu, 31 May 2001 21:20:40 -0300 (ADT) X-Authentication-Warning: mailserv.mta.ca: Majordom set sender to cat-dist@mta.ca using -f From: Sandra Groszmann Date: Thu, 31 May 2001 15:28:17 +0200 (MET DST) Message-Id: <200105311328.PAA02157@pink.inf.tu-dresden.de> To: stacs-mailliste@tcs.inf.tu-dresden.de Subject: categories: Weighted Automata: Workshop Announcement X-Sun-Charset: US-ASCII MIME-Version: 1.0 Content-Type: Text/plain; charset="US-ASCII" Content-Transfer-Encoding: 7bit Sender: cat-dist@mta.ca Precedence: bulk Status: O X-Status: X-Keywords: X-UID: 65 [apologies if you receive multiple copies of this message] ----------------------------------------------------------------------------- Weighted Automata: Theory and Applications Dresden University of Technology, March 4 - 8, 2002 The workshop will cover all aspects of weighted automata, ranging from the theory of formal power series to max-plus-algebra and applications as e.g. in algebraic optimization of railway networks or natural language processing. The aim is to present tutorials and survey lectures by outstanding scientists in this area. Moreover, we encourage everybody to participate in this work- shop and present their own technical contribution in this area. We are happy to announce the following tutorials and survey lectures: Tutorials: Survey lectures: S. Gaubert (INRIA, Paris) S. Bloom (Hoboken, New Jersey) D. Kozen (Ithaca) Z. Esik (Szeged) W. Kuich (Wien) Z. F\"ul\"op (Szeged) M. Mohri (AT&T, New Jersey) P. Gastin (Paris), provisionally B. F. Heidergott (Eindhoven) B. Khoussainov (Auckland) G. J. Olsder (Delft) I. Petre (Turku) E. Stark (Stony Brook, New York) K. Zimmermann (Prague) All lecturers are asked to give a survey on their field of interest followed by recent research results. Interested participants are most welcome. If you wish to present a technical contribution, please send us an abstract (preferably of at most one page) before December 1, 2001. Authors will be informed about acceptance of their submission before December 15, 2001. Deadline for registration is February 1, 2001. There are no conference fees. Call for papers: There will be a special issue of the Journal of Automata, Languages, and Combinatorics (JALC) on the topic of this workshop. The deadline for submission of papers is April 20, 2002. All submissions will be refereed according to the usual journal standards. For further information see http://www.orchid.inf.tu-dresden.de/gk-spezifikation/wata.html ------------------------------------------------------------------------------ Manfred Droste Heiko Vogler Dresden University of Technology Dresden University of Technology Institute of Algebra Institute of Theor. Computer Science D-01062 Dresden, Germany D-01062 Dresden, Germany Tel.: +49-351-463-3908 Tel.: +49-351-463-8232 Fax: +49-351-463-4235 Fax: +49-351-463-8504 E-Mail: droste@math.tu-dresden.de E-Mail: vogler@inf.tu-dresden.de