From cat-dist Wed May 6 20:51:50 1998 Received: (from Majordom@localhost) by mailserv.mta.ca (8.8.8/8.8.8) id UAA04461 for categories-list; Wed, 6 May 1998 20:02:34 -0300 (ADT) X-Authentication-Warning: mailserv.mta.ca: Majordom set sender to cat-dist@mta.ca using -f Date: Wed, 6 May 1998 18:15:06 -0400 (EDT) X-Sender: awodey@cyrus.andrew.cmu.edu Message-Id: Mime-Version: 1.0 Content-Type: text/plain; charset="us-ascii" To: categories@mta.ca From: Steve Awodey Subject: categories: preprint available Cc: Alex.Simpson@dcs.ed.ac.uk, d.cubric@pmms.cam.ac.uk Sender: cat-dist@mta.ca Precedence: bulk Status: O X-Status: Dear Colleagues, The preprint mentioned below is available from my page on the WWW, http://www.andrew.cmu.edu/user/awodey/ Please let me know if you have difficulty obtaing or printing it, or if you would like to have a paper copy sent. Steve A. ******************************************************************************* "Topological representation of the lambda-calculus" S. Awodey Abstract: The lambda-calculus can be represented topologically by assigning certain spaces to the types and certain continuous maps to the terms. Using a recent result from topos theory, the usual calculus of lambda-conversion is shown to be deductively complete with respect to such topological semantics. It is also shown to be functionally complete, in the sense that there is always a ``minimal'' topological model, in which every continuous function is lambda-definable. These results subsume earlier ones using cartesian closed categories, as well as those employing so-called Henkin and Kripke lambda-models. ******************************************************************************* From cat-dist Wed May 6 20:51:55 1998 Received: (from Majordom@localhost) by mailserv.mta.ca (8.8.8/8.8.8) id UAA05039 for categories-list; Wed, 6 May 1998 20:03:15 -0300 (ADT) X-Authentication-Warning: mailserv.mta.ca: Majordom set sender to cat-dist@mta.ca using -f Message-ID: <3550BCF2.1B7@iswest.com> Date: Wed, 06 May 1998 15:41:38 -0400 From: Zhaohua Luo X-Mailer: Mozilla 3.01 (Win95; I) MIME-Version: 1.0 To: categories@mta.ca Subject: categories: abstract algebraic geometry Content-Type: text/plain; charset=us-ascii Content-Transfer-Encoding: 7bit Sender: cat-dist@mta.ca Precedence: bulk Status: O X-Status: Please visit my home page Categorical Geometry (www.iswest.com/~zack) for the newly posted paper Categorical Geometry: 1 Analytic Categories Regards, Z. Luo From cat-dist Wed May 6 20:53:00 1998 Received: (from Majordom@localhost) by mailserv.mta.ca (8.8.8/8.8.8) id TAA04743 for categories-list; Wed, 6 May 1998 19:46:51 -0300 (ADT) X-Authentication-Warning: mailserv.mta.ca: Majordom set sender to cat-dist@mta.ca using -f Message-ID: <354F1398.E7BAC0E1@dcs.qmw.ac.uk> Date: Tue, 05 May 1998 14:26:49 +0100 From: "David J. Pym" Organization: Queen Mary & Westfield College, University of London X-Mailer: Mozilla 4.04 [en] (X11; I; Linux 2.0.30 i586) MIME-Version: 1.0 To: bra-types@cs.chalmers.se, categories@mta.ca, lfp@dcs.qmw.ac.uk, alc@dcs.qmw.ac.uk Subject: categories: CADE-15 Workshop: Proof-search in type-theoretic languages. Content-Type: text/plain; charset=us-ascii Content-Transfer-Encoding: 7bit Sender: cat-dist@mta.ca Precedence: bulk Status: O X-Status: [ Apologies to those who receive this many times through different channels ] Dear colleague, Please find enclosed the Last Call for Contributions for the CADE-15 Workshop on "Proof-search in Type-theoretic Languages", 5th July, 1998 (Lindau, Germany). Extended Deadline: May 18, 1998. Information: http://www.loria.fr/~galmiche/cade15-wpsttl.html Best regards Didier Galmiche ----------------------------------------------------------------- LAST CALL FOR CONTRIBUTIONS CADE-15 Workshop on PROOF SEARCH IN TYPE-THEORETIC LANGUAGES Lindau, Germany July 5, 1998 EXTENDED DEADLINE FOR SUBMISSION: May 18, 1998 A one day workshop on "Proof Search in Type-Theoretic Languages" will be held the 5th July 1998 in conjunction with the 15th Conference in Automated DEduction (CADE-15, Lindau, Germany). Attendance is by invitation only: authors of accepted submissions will be invited. Hardcopies of the preliminary proceedings will be distributed at the workshop. Proceedings will be published (depending on the number of high-quality papers) as a volume in Electronic Notes in Theoretical Computer Science, Elsevier Science Publishers. TOPICS Much recent work has been devoted to type theory and its applications to proof and program development in various logical frameworks. This workshop focuses on proof search in type-theoretic languages and their underlying logics(e.g., classical, intuitionistic, linear logics). Such languages are logical frameworks for representing proofs and in some cases formalize connections between proofs and programs that support program synthesis. The objective of the workshop is to provide an integrated forum for the presentation of research and the exchange of ideas and experiences in proof search in type-theoretic languages and related logics or logical frameworks. Topics of interest, in this context, include (but are not restricted to): - foundations and semantics of proof search, - methods, techniques and concepts related to proof construction, - logic programming as search-based computation, integration of model-theoretic semantics, - proof synthesis vs program synthesis, - applications, - equational theories and rewriting, - decision procedures, complexity results, - environments for formal proof development. SUBMISSIONS Researchers interested in presenting their works are invited to send an extended abstract (8-10 pages)} by e-mail submissions of Postscript files to the Program Chair (Didier.Galmiche@loria.fr) before May 14, 1998. Researchers interested in attending the workshop (without giving a presentation) should send a position paper (1-2 pages) presenting their interest. Papers will be reviewed by peers, typically members of the program committee. Additional information will be available through WWW address: http://www.loria.fr/~galmiche/cade15-wpsttl.html PROGRAM COMMITTEE: D. Galmiche (LORIA & UHP, Nancy) - Program Chair P. Lincoln (SRI, Stanford) F. Pfenning (CMU, Pittsburgh) D. Pym (Queen Mary & Westfield College, Univ. London) T. Tammet (Chalmers Univ, Goeteborg) IMPORTANT DATES Deadline for submissions: May 18, 1998 Notification of acceptance: May 30, 1998 Workshop handouts ready: June 12, 1998 Workshop date: July 5, 1998 INFORMATION Program Chair Didier Galmiche LORIA - CNRS & UHP Nancy I B\^atiment LORIA 54506 Vandoeuvre-les-Nancy France Phone: +33 3 83 59 20 15 Fax: +33 3 83 41 30 79 email: Didier.Galmiche@loria.fr URL: http://www.loria.fr/~galmiche/cade15-wpsttl.html From cat-dist Sun May 10 13:26:43 1998 Received: (from Majordom@localhost) by mailserv.mta.ca (8.8.8/8.8.8) id MAA05250 for categories-list; Sun, 10 May 1998 12:17:41 -0300 (ADT) X-Authentication-Warning: mailserv.mta.ca: Majordom set sender to cat-dist@mta.ca using -f Date: Thu, 7 May 1998 15:25:22 -0400 (EDT) X-Sender: awodey@cyrus.andrew.cmu.edu Message-Id: Mime-Version: 1.0 Content-Type: text/plain; charset="us-ascii" To: categories@mta.ca From: Steve Awodey Subject: categories: more precisely ... Sender: cat-dist@mta.ca Precedence: bulk Status: O X-Status: Dear Colleagues, Since this is the categories list, I could and should have been more specific about the contents of the preprint I announced yesterday: "Topological representation of the lambda-calculus", available from my page on the WWW, http://www.andrew.cmu.edu/user/awodey/ In a nut-shell, the point is that the Butz-Moerdijk spatial covering theorem for topoi can be used to embed any CCC fully and faithfully (and CC) into a topos of sheaves on a space. So the "topological semantics" mentioned are actually in such topoi of sheaves. Steve A. From cat-dist Sun May 10 13:26:55 1998 Received: (from Majordom@localhost) by mailserv.mta.ca (8.8.8/8.8.8) id MAA05021 for categories-list; Sun, 10 May 1998 12:15:15 -0300 (ADT) X-Authentication-Warning: mailserv.mta.ca: Majordom set sender to cat-dist@mta.ca using -f Date: Thu, 7 May 1998 18:40:20 +0200 (MET DST) Message-Id: <199805071640.SAA15338@harald.daimi.aau.dk> From: Uffe Henrik Engberg To: categories@mta.ca Subject: categories: ICALP'98: Call for Participation Mime-Version: 1.0 (generated by tm-edit 7.106) Content-Type: text/plain; charset=ISO-8859-1 Content-Transfer-Encoding: 8bit Sender: cat-dist@mta.ca Precedence: bulk Status: O X-Status: CALL FOR PARTICIPATION ICALP'98 25th International Colloquium on Automata, Languages, and Programming Aalborg, Denmark July 13-17, 1998 http://www.cs.auc.dk/icalp98/ The International Colloquium on Automata, Languages, and Programming (ICALP) is the annual conference series of the European Association for Theoretical Computer Science (EATCS). It is intended to cover all important areas of theoretical computer science. During 5 conference days and two weekends, ICALP will give you the opportunity to choose between 70 regular papers, 9 invited lectures, including the Gödel award lecture, and 4 thematic workshops and one associated summer school offering dozens of more talks! The deadline for early registration is May 22! Please register NOW! The final deadline for registration is June 12. The full programme and registration form are available at the web address above and from the organizers (just send a message to icalp98@cs.auc.dk or a fax to +45 98159889). Kim Guldstrand Larsen ICALP Conference chair BRICS Department of Computer Science Aalborg University Fredrik Bajersvej 7 9220 Aalborg DENMARK Tel.: +45 96 35 88 93 (direct) From cat-dist Sun May 10 13:31:12 1998 Received: (from Majordom@localhost) by mailserv.mta.ca (8.8.8/8.8.8) id MAA04093 for categories-list; Sun, 10 May 1998 12:26:39 -0300 (ADT) X-Authentication-Warning: mailserv.mta.ca: Majordom set sender to cat-dist@mta.ca using -f Message-ID: <3554299D.CE113D0B@obelix.ee.duth.gr> Date: Sat, 09 May 1998 13:02:06 +0300 From: Apostolos Syropoulos X-Mailer: Mozilla 4.05 [en] (X11; I; Linux 2.1.99 i586) MIME-Version: 1.0 To: categories@mta.ca Subject: categories: Multicategories Content-Type: multipart/alternative; boundary="------------5231419DBEC2411F357EAB83" Sender: cat-dist@mta.ca Precedence: bulk Status: O X-Status: --------------5231419DBEC2411F357EAB83 Content-Type: text/plain; charset=x-UNICODE-2-0-UTF-7 Content-Transfer-Encoding: 7bit Dear Category Theorists, I am currently studying a paper on logic and the author employs category theory in his work. However, he is using "multicategories" which is something I hear for the first time. Unfortunately my knowledge of CT isn't that deep and so if someone could suggest me papers/books that provide a definition of this term, I would be really grateful to him/her! Yours Sincerely, A. S. -- **************************************************************** *Apostolos Syropoulos * *snail mail: 366, 28th October Str., GR-671 00 Xanthi, HELLAS * *email : apostolo@obelix.ee.duth.gr * *phone num.: +-30-(0)541-28704 * *home page : http://obelix.ee.duth.gr/+AH4-apostolo * **************************************************************** --------------5231419DBEC2411F357EAB83 Content-Type: text/html; charset=x-UNICODE-2-0-UTF-7 Content-Transfer-Encoding: 7bit      Dear Category Theorists,

     I am currently studying a paper on logic and the author employs category theory in his work. However, he is using
"multicategories" which is something I hear for the first time.
Unfortunately my knowledge of CT isn't that deep and so
if someone could suggest me papers/books that provide
a definition of this term, I would be really grateful to him/her!

Yours Sincerely,

A. S. 

-- 
****************************************************************
*Apostolos Syropoulos                                          *
*snail mail: 366, 28th October Str., GR-671 00  Xanthi, HELLAS *
*email     : apostolo@obelix.ee.duth.gr                        *
*phone num.: +-30-(0)541-28704                                  *
*home page : http://obelix.ee.duth.gr/+AH4-apostolo                *
****************************************************************
  --------------5231419DBEC2411F357EAB83-- From cat-dist Tue May 12 13:29:55 1998 Received: (from Majordom@localhost) by mailserv.mta.ca (8.8.8/8.8.8) id KAA12465 for categories-list; Tue, 12 May 1998 10:22:25 -0300 (ADT) X-Authentication-Warning: mailserv.mta.ca: Majordom set sender to cat-dist@mta.ca using -f Reply-To: frode@odegard.com (Frode Odegard) From: "Frode Odegard" Message-Id: <9805111226.ZM4174@home.odegard.com> Date: Mon, 11 May 1998 12:26:46 -0700 In-Reply-To: Barry Jay "the FISh language" (May 11, 10:27pm) References: <199805111508.KAA12135@cslinux1.cs.indiana.edu> X-Mailer: Z-Mail (3.2.3 08feb96 MediaMail) To: types-errors@cs.indiana.edu, skeletons@dcs.edinburgh.ac.uk, types@cs.indiana.edu, categories@mta.ca, it-announce@staff.cs.su.oz.au, staff@socs.uts.edu.au, researchers@socs.uts.edu.au Subject: categories: Re: the FISh language Mime-Version: 1.0 Content-Type: text/plain; charset=us-ascii Sender: cat-dist@mta.ca Precedence: bulk Status: O X-Status: The right URL appears to be: http://www-staff.socs.uts.EDU.AU:8080/~cbj/FISh/Announcement/ Best regards, Frode Odegard -- .......................................................... Frode Odegard - frode@odegard.com - http://www.odegard.com From cat-dist Tue May 12 13:37:31 1998 Received: (from Majordom@localhost) by mailserv.mta.ca (8.8.8/8.8.8) id KAA10795 for categories-list; Tue, 12 May 1998 10:23:35 -0300 (ADT) X-Authentication-Warning: mailserv.mta.ca: Majordom set sender to cat-dist@mta.ca using -f X-Received: from aragorn.ics.muni.cz (aragorn.ics.muni.cz [147.251.4.33]) by mailserv.mta.ca (8.8.8/8.8.8) with ESMTP id IAA05519 for ; Tue, 12 May 1998 08:03:42 -0300 (ADT) X-Received: from queen.math.muni.cz (queen.math.muni.cz [147.251.80.1]) by aragorn.ics.muni.cz (8.8.5/8.8.5) with SMTP id NAA01397 for ; Tue, 12 May 1998 13:03:18 +0200 (MET DST) X-Received: by queen.math.muni.cz id AA05835 (5.67a8/IDA-1.4.4 for cat-dist@mta.ca); Tue, 12 May 1998 12:56:41 +0200 From: Jiri Rosicky Message-Id: <199805121056.AA05835@queen.math.muni.cz> Subject: categories: PSSL 68 To: cat-dist@mta.ca Date: Tue, 12 May 1998 12:56:41 +0200 (MET DST) X-Mailer: ELM [version 2.4ME+ PL25 (25)] Mime-Version: 1.0 Content-Type: text/plain; charset=US-ASCII Content-Transfer-Encoding: 7bit Sender: cat-dist@mta.ca Precedence: bulk Status: RO X-Status: ********* First Announcement ********* The 68th Peripatetic Seminar on Sheaves and Logic August 29-30, 1998 Brno, Czech Republic The 68th meeting of the PSSL will be held at the Masaryk University, Brno, Czech Republic over the weekend of 29-30 August 1998. It is organized in connection with the federated conferences MFCS (Mathematical Foundations of Computer Science) and CSL (Computer Science Logic) which are taking place in Brno during August 23-28, 1998. There are other workshops related to MFCS\CSL and participants interested to stay in Brno the whole week may contact Jan Staudek. As usual, the 68th meeting of the PSSL will be informal in nature and it will be focused on category theory, logic and theoretical computer science. We have arranged an accommodation in a student dormitory (single rooms, for 2 nights since Friday to Sunday) together with breakfasts and lunches in a university restaurant. The cost is 80$ for those who will register till June 25th and 120$ for others. Participants wishing to stay in hotels should contact Jan Staudek. Brno is located about 200 km south-east of Prague and 130 km north of Vienna and it can be reached from the both airports by trains and buses. More details will be available in the second announcement. We will maintain a www-page containing all informations. The registrations for PSSL 68 are handled electronically via web, on http://www.fi.muni.cz/usr/staudek/mfcs/, or via e-mail. To use the web, all you have to do is to carefully fill out the form located there using Netscape 2.0 / Explorer 3.0 or later (with Java Script enabled). To register via e-mail, please fill out the form below and return it (preferably by e-mail) to Jan Staudek (staudek@fi.muni.cz). We would be pleased if you could register till June 25th. Looking forward to meeting you in Brno. Jiri Rosicky and Jan Paseka Postal address: Jan Paseka Department of Mathematics Masaryk University Janackovo nam. 2a 66295 Brno Czech Republic email: paseka@math.muni.cz www: http://www.math.muni.cz/ftp/ftp/pub/math/people/Paseka/pssl68/pssl68.html (the both addresses can be used for everything concerning PSSL, except the registration) _________________________________________________________________ 68th PSSL/MFCS Registration Form (e-mail) ----------------------------------------- I want to attend the 68th PSSL in Brno Name: Address: email: I wish to give a talk entitled: I wish to have the PSSL accommodation and meals: Special dietary requirements: __________________ Method of payment (all payment in US dollars): ---------------------------------------------- [] VISA [] MASTERCARD [] EUROCARD Please note that the amount your card will be charged depends on the actual change rate. Please make signed this Registration Form and send it to Faculty of Informatics MU MFCS, Jan Staudek Botanicka 68a 602 00 Brno, Czech Republic Amount to be payed: ________________ Cardholder's name: ---------------- Card no.: _________________ Exp: __/__/__ Sign:_____________________ [] Bank Checque / Eurochecque Please make check payable in US dollars to "Faculty of Informatics, Masaryk University" enclosed to signed this Registration Form and send all to Faculty of Informatics MU MFCS, Jan Staudek Botanicka 68a 602 00 Brno, Czech Republic Sign:_____________________ [] Bank transfer to Komercni banka, a.s. pobocka Brno-mesto nam. Svobody 21 631 31 Brno, Czech Republic SWIFT Code: KOMBCZPP Account Number: 85636621/0100 Account Number: 1234567890-1234567890 Details of Payment (Mandatory): 3375000498, < name > Be sure to clearly state 3375000498 and your name in Details of Payment. Amount of Payment : $ __________ Amount of Payment : __________ Kc For Czech participants (in accordance with current currency rate) Expected Date of Payment : ------------ _______________________________________________________________ ----- End of forwarded message from Jan Paseka ----- From cat-dist Tue May 12 13:49:33 1998 Received: (from Majordom@localhost) by mailserv.mta.ca (8.8.8/8.8.8) id KAA11573 for categories-list; Tue, 12 May 1998 10:22:54 -0300 (ADT) X-Authentication-Warning: mailserv.mta.ca: Majordom set sender to cat-dist@mta.ca using -f Date: Mon, 11 May 1998 22:27:43 +1000 (EST) Message-Id: <199805111227.WAA03019@algae.socs.uts.EDU.AU> To: skeletons@dcs.edinburgh.ac.uk, types@cs.indiana.edu, categories@mta.ca, it-announce@staff.cs.su.oz.au, staff@socs.uts.edu.au, researchers@socs.uts.edu.au Subject: categories: the FISh language From: Barry Jay Sender: cat-dist@mta.ca Precedence: bulk Status: RO X-Status: [apologies for multiple announcements] *********************************** * Functional = Imperative + Shape * *********************************** FISh is a new array programming language that combines (and extends) the EXPRESSIVE POWER of functional programming with the EFFICIENT EXECUTION of imperative, or procedural, programming by performing STATIC SHAPE ANALYSIS on all programs. This shape computation reduces higher-order functional programs to simple imperative forms, i.e. F - Sh = I. Conversely, FISh works best when functions are constructed from imperative procedures and shape functions, as recommended by the slogan that gives the language its name. F = I + Sh FISh execution speeds on typical array problems are SEVERAL TIMES FASTER than other higher-order, polymorphic languages. This announcement, research papers, reference material and the implementation are all available from http://linus.socs.uts.edu.au/~cbj/FISh/announcement.html The main themes are introduced in the paragraphs below. Barry Jay http://linus.socs.uts.edu.au/~cbj *********************************** Expressive Power ~~~~~~~~~~~~~~~~ FISh supports - the usual functional features such as strong typing, higher-order functions and parametric polymorphism. It also supports - simple imperative features such as assignment, for- and while-loops, and local variables, using a type of commands. Procedures are represented as functions into commands, as in Algol-like languages. Unlike existing Algol-like languages, it also supports data types of arrays, so that array programs may be polymorphic in the size of the array. Now this has been extended to support - poly-dimensional array programming. If a is any array type then [a] is the type of all arrays with entries in a that are - finite dimensional, and - regular, such as vectors, matrices, three-dimensional arrays, etc. Thus, poly-dimensional array programs can be written that act on a vector, matrix, or higher-dimensional array. For example, the standard prelude supports a polymorphic constant map : (a -> b) -> [a] -> [b] which will map a function over a vector, matrix, or higher-dimensional array. Note that a matrix of integers, or type [int] has a different type from a vector of vectors of type [[int]]. Thus, given sum_int : [int] -> int which adds up an array of integers, we have map sum_int : [[int]] -> [int] which will sum each entry of the outer array. This is useful when - representing complex numbers as arrays of length 2, or - each entry in an array has an associated array of data, e.g. - each entry is given an array of nearest neighbours, or - decomposing an array into an array of blocks, e.g. - a matrix into a matrix of matrices. Efficiency ~~~~~~~~~~ ------------------------------------------------------------- | |Map Reduce Q'sort FFT MM-loops MM-ip | |_______________|____________________________________________| |---------------|--------------------------------------------| |FISh |1.04 0.37 1.93 3.57 4.36 7.05 | |---------------|--------------------------------------------| |Ocaml(in-lined)|4.00 2.66 3.53 | |---------------|--------------------------------------------| |Ocaml |5.99 4.59 15.47 8.16 7.71 60.61 | |---------------|--------------------------------------------| |speedup |5.8 12.4 8.0 2.3 1.8 8.6 | -------------------------------------------------------------- Benchmark user times See http://linus.socs.uts.edu.au/~cbj/FISh/Benchmarks for more details. Static Shape Analysis ~~~~~~~~~~~~~~~~~~~~~ Shape analysis is used to determine the number of dimensions, and the size in each dimension, of every array appearing in a program. (A program is a closed term of array or command type.) In particular, it checks that every array is regular, i.e. is a hyper-cube whose entries all have the same shape. The latter requirement is necessary to ensure that every entry in a vector of vectors has the same length, i.e. that a vector of vectors is a matrix. As well as detecting irregularities, it is able to detect all other shape errors, such as multiplying matrices of innapropriate sizes, or having incompatible numbers of dimensions. It is the power of shape analysis that makes poly-dimensional programming feasible. Knowledge of the shapes can be used to improve memory management during compilation of the resulting imperative program. In particular, FISh supports a clear stack discipline, and so does not require a garbage collector. The existing FISh compiler translates programs in to simple C code, which is then compiled and executed in the usual way. This approach is also being applied in the design and implementation of a parallel version of FISh, called GoldFISh. F = I + Sh ~~~~~~~~~~ The slogan is represented within the standard prelude by a function proc2fun : (var a -> var b -> comm) -> (#b -> #a) -> b -> a for converting procedures (and shapes) to functions. proc2fun pr sh x uses the shape function sh and the shape #x of the array x to determine the shape of the result. It then creates a local variable y of this shape, and invokes the procedure pr on and a stored value of x, finally returning the value of y. Semantics ~~~~~~~~~ Shape analysis is supported by a clean and powerful categorical semantics, in which the shape-data (or shape-entry) decomposition is represented by a pullback. For multi-dimensional arrays, this is entries [a] ---------> List a | | | |___| | shape | | map # | | \/ \/ List N x #a -----> List #a c where c takes the list of numbers ns and the a-shape sh and produces a list of length given by the product of ns whose entries are all sh. In other words, all entries of an array must have the same shape. Poly-dimensionality ~~~~~~~~~~~~~~~~~~~ FISh supports the usual Hindley-Milner style of polymorphism. It also supports polymorphism in array sizes (unlike earlier Algol-like languages) and in the number of dimensions of an array. That is, FISh supports polydimensional programming. For example, the map function is defined to have type map : (a -> b) -> [a] -> [b] and so may act on a vector, matrix or higher-dimensional array. However, the existence of the simple imperative features means that this can be compiled into a sequence of nested for-loops corresponding to the number of dimensions of the array argument. Polydimensionality is a form of *shape polymorphism*. Array Programming ~~~~~~~~~~~~~~~~~ Poly-dimensionality means that many array programs, e.g. numerical recipes, can be written for any number of dimensions while maintaining static type and shape checking. For example, FISh supports poly-dimensional stencilling and a poly-dimensional difference equation solver (see Sample Programs). Parallel Programming ~~~~~~~~~~~~~~~~~~~~ Size and shape are important parameters in estimating the cost of alternative parallel implementations. FISh has been designed to support a parallel variant, called GoldFISh, currently under development. GoldFISh will support additional parallel combinators for some of the existing FISh functions that express the usual second-order constants and also the usual array distributions (see Sample Programs). *********************************** From cat-dist Mon May 18 23:27:14 1998 Received: (from Majordom@localhost) by mailserv.mta.ca (8.8.8/8.8.8) id WAA02091 for categories-list; Mon, 18 May 1998 22:34:19 -0300 (ADT) X-Authentication-Warning: mailserv.mta.ca: Majordom set sender to cat-dist@mta.ca using -f X-SMTP-Posting-Origin: Math.McGill.CA (Gauss.Math.McGill.CA [132.206.150.3]) Date: Tue, 12 May 1998 15:40:16 -0400 (EDT) From: Michael MAKKAI To: Apostolos Syropoulos Cc: categories@mta.ca Subject: Re: categories: Multicategories In-Reply-To: <3554299D.CE113D0B@obelix.ee.duth.gr> Message-Id: Mime-Version: 1.0 Content-Type: TEXT/PLAIN; charset=US-ASCII Sender: cat-dist@mta.ca Precedence: bulk Status: O X-Status: On Sat, 9 May 1998, Apostolos Syropoulos wrote: > Dear Category Theorists, > > I am currently studying a paper on logic and the author employs > category theory in his work. However, he is using > "multicategories" which is something I hear for the first time. > Unfortunately my knowledge of CT isn't that deep and so > if someone could suggest me papers/books that provide > a definition of this term, I would be really grateful to him/her! > > Yours Sincerely, > > A. S. > > -- > **************************************************************** > *Apostolos Syropoulos * > *snail mail: 366, 28th October Str., GR-671 00 Xanthi, HELLAS * > *email : apostolo@obelix.ee.duth.gr * > *phone num.: +-30-(0)541-28704 * > *home page : http://obelix.ee.duth.gr/+AH4-apostolo * > **************************************************************** > > > Here are two references to multicategories, both by Joachim Lambek: "Deductive systems and categories II", Springer Lecture Notes in Mathematics. no.86, pp. 76-122 (1969) "Multicategories revisited", In: Categories in Computer Science and Logic, Proceedings, Boulder 1987; Contemporary Math 92, AMS; pp. 217-240 (1989). Michael Makkai From cat-dist Mon May 18 23:27:19 1998 Received: (from Majordom@localhost) by mailserv.mta.ca (8.8.8/8.8.8) id WAA02322 for categories-list; Mon, 18 May 1998 22:37:00 -0300 (ADT) X-Authentication-Warning: mailserv.mta.ca: Majordom set sender to cat-dist@mta.ca using -f X-Received: from rs2.hrz.tu-darmstadt.de (rs2.hrz.tu-darmstadt.de [130.83.22.63]) by mailserv.mta.ca (8.8.8/8.8.8) with SMTP id JAA02348 for ; Wed, 13 May 1998 09:00:51 -0300 (ADT) X-Received: from fb0430.mathematik.th-darmstadt.de (daemon@fb0430.mathematik.tu-darmstadt.de [130.83.2.30]) by rs2.hrz.tu-darmstadt.de (8.6.12/8.6.12.1ms) with ESMTP id MAA13216 for ; Wed, 13 May 1998 12:18:34 +0200 X-Received: from fb0448.mathematik.tu-darmstadt.de by fb0430.mathematik.th-darmstadt.de (1.37.109.20/Server-1.5/HRZ-THD) id AA254714711; Wed, 13 May 1998 12:18:32 +0200 X-Received: by fb0448.mathematik.tu-darmstadt.de (1.37.109.20/Client-1.5/HRZ-THD) id AA091814709; Wed, 13 May 1998 12:18:29 +0200 From: Thomas Streicher Message-Id: <199805131018.AA091814709@fb0448.mathematik.tu-darmstadt.de> Subject: categories: fibrational theory of geometric morphisms To: cat-dist@mta.ca Date: Wed, 13 May 1998 12:18:29 MESZ X-Mailer: Elm [revision: 109.19] Sender: cat-dist@mta.ca Precedence: bulk Status: O X-Status: A(n attempt of a) systematic exposition of the basics of a Fibrational Theory of Geometric Morphisms based essentially on the work of B'enabou, Moens et. al. can be found in the diploma thesis of my student Peter Lietz under the www-address http://www.mathematik.tu-darmstadt.de/ags/ag14/mitglieder/lietz-de.html A new aspect seems to be that Moens' characterisation of geometricity of a fibration is essentially extensivity of the fibred category albeit w.r.t. internal sums. Thomas Streicher From cat-dist Mon May 18 23:27:23 1998 Received: (from Majordom@localhost) by mailserv.mta.ca (8.8.8/8.8.8) id WAA03845 for categories-list; Mon, 18 May 1998 22:36:13 -0300 (ADT) X-Authentication-Warning: mailserv.mta.ca: Majordom set sender to cat-dist@mta.ca using -f From: pareigis@math02.mathematik.uni-muenchen.de Message-Id: <9805170659.AB08536@math02> Comments: Authenticated sender is To: categories@mta.ca Date: Sun, 17 May 1998 08:00:58 +0000 Subject: categories: Who said: General Abstract Nonsense X-Mailer: Pegasus Mail for Windows (v2.54) Sender: cat-dist@mta.ca Precedence: bulk Status: O X-Status: Hi - who coined the expression General Abstract Nonsense as a synonym for category theory? Where did it first appear in print? Thanks for any comments. Bodo -------------------------------------------------------------------- Prof. Dr. Bodo Pareigis Dept.of Mathematics, University of Munich Theresienstr. 39, D-80333 Muenchen, GERMANY ........................................... Email: pareigis@rz.mathematik.uni-muenchen.de Web: http://www.mathematik.uni-muenchen.de/~pareigis phone: office: +49 89-2394-4426 From cat-dist Mon May 18 23:27:24 1998 Received: (from Majordom@localhost) by mailserv.mta.ca (8.8.8/8.8.8) id WAA03096 for categories-list; Mon, 18 May 1998 22:35:21 -0300 (ADT) X-Authentication-Warning: mailserv.mta.ca: Majordom set sender to cat-dist@mta.ca using -f Date: Wed, 13 May 1998 15:35:53 +0200 From: gaucher@irma.u-strasbg.fr (Philippe Gaucher) Message-Id: <199805131335.PAA22813@irma.mathstras> To: categories@mta.ca Subject: categories: question about omega-category Mime-Version: 1.0 Content-Type: text/plain; charset=us-ascii Content-MD5: zzritXrJDCVYue0PACU2qA== Content-Transfer-Encoding: 8bit X-MIME-Autoconverted: from base64 to 8bit by mailserv.mta.ca id LAA29889 Sender: cat-dist@mta.ca Precedence: bulk Status: O X-Status: Dear categorician (or categorist, I do not know the word in English), I posted the following question some days ago in sci.math.research. Maybe this list is more appropirated : I would need to understand a proof of the following proposition : There is only one functor up to isomorphism TENS : omega-Cat x omega-Cat -> omega-Cat for which C TENS - and - TENS C have right adjoint for every omega-category C and which satisfies I^p TENS I^q = I^{p+q} where I^p is the omega-category canonically associated to the p-cube, (using for example the set of composable sub pasting schemes of the pasting scheme associated to the p-cube). I have a paper from Crans ("Pasting schemes for the monoidal biclosed structure on omega-Cat") which proves explicitely the proposition. I do not understand the construction, which is very technical (*). Is there a less complicated way to prove this proposition ? I do not need an explicit construction. Any help is welcome. pg. (*) What is a pasting presentation for example ? I know the definition of pasting scheme, realization of pasting schemes, but I do not know the one of "pasting presentation". Another question : if f, g are morphisms in C and h, k morphisms in D, is there in C TENS D elements corresponding to f TENS h and g TENS k, and if the answer is yes, is it true that (f TENS h) o_p (g TENS k) = (f o_p g) TENS (h o_p k) ? I suppose that it is false : if it should be true, why the construction of this monoidal structure is so complicated ? From esik@inf.u-szeged.hu Tue May 12 11:10:31 1998 Received: from inf.u-szeged.hu (csilla.inf.u-szeged.hu [160.114.37.74]) by mailserv.mta.ca (8.8.8/8.8.8) with SMTP id LAA15395 for ; Tue, 12 May 1998 11:10:21 -0300 (ADT) From: esik@inf.u-szeged.hu Message-Id: <199805121410.LAA15395@mailserv.mta.ca> Date: Tue, 12 May 98 16:09 MET To: rrosebrugh@mta.ca Status: RO X-Status: >From esik Tue May 12 16:09:55 +0200 1998 remote from inf.u-szeged.hu To: rrosebrugh@mta.ca cc: esik Subject: FICS 2nd announcement Date: Tue, 12 May 1998 16:09:55 +0200 From: Esik Zoltan Received: from inf.u-szeged.hu by inf.u-szeged.hu; Tue, 12 May 1998 16:09 MET Content-Type: text Content-Length: 4630 Dear Professor Rosebrugh, Would you please forward the attached 2nd announcement of the FICS workshop to the subsribers of categories. Thank you in advance. Yours sincerely, Zoltan Esik ******************************************************************************* ******************************************************************************* ** ** ** F I C S ' 9 8 ** ** ** ** Fixed Points in Computer Science ** ** ** ** A Satellite Workshop to MFCS'98 ** ** ** ** August 27-28, 1998, Brno, Czech Republic ** ** ** ** Second Announcement ** ** ** ******************************************************************************* ******************************************************************************* Aim: Fixed points play a fundamental role in several areas of computer science, and the construction and properties of fixed points have been investigated in many different frameworks. The aim of the workshop is to provide a forum for researchers to present their results to those members of the computer science community who study or apply the fixed point operation in the different fields and formalisms. Topics: Construction and reasoning about properties of fixed points, categorical, metric and ordered fixed point models, continuous algebras, relation algebras, fixed points in process algebras and process calculi, regular algebra of finitary and infinitary languages, formal power series, tree automata and tree languages, infinite trees, the mu-calculus and other programming logics, fixed points in relation to dataflow and circuits, fixed points and the lambda calculus. Invited lectures: A. Arnold (Bordeaux): Boolean mu-calculus and its relations with model-checking and games J. W. de Bakker (Amsterdam): Fixed points in metric semantics Y. N. Moschovakis (Los Angeles/Athens): Fair, non-deterministic recursion in higher types (tentative) Program Committee: R. Backhouse (Eindhoven) S. L. Bloom (Hoboken) C. Boehm (Rome) R. De Nicola (Florence) Z. Esik (Szeged, chairman) P. Freyd (Philadelphia) I. Guessarian (Paris) D. Kozen (Cornell) W. Kuich (Vienna) M. Mislove (Tulane) R. F. C. Walters (Sydney) Contact person: Zoltan Esik Dept. of Computer Science Jozsef Attila University P.O.B. 652 6701 Szeged, Hungary e-mail: fics@inf.u-szeged.hu phone: ++36-62-454-289 fax: ++36-62-312-292 Paper submission: Authors are invited to send three copies of an abstract not exceeding three pages to the PC chair. Electronic submissions in the form of uuencoded postscript file are encouraged and can be sent to fics@inf.u-szeged.hu. Submissions are to be received before May 25, 1998. Authors will be notified of acceptance by June 25, 1998. Proceedings: Preliminary proceedings containing the abstracts of the talks will be available at the meeting. Publication of final proceedings as a special issue of Theoretical Informatics and Applications depends on the number and quality of the papers. The workshop will be organised at the same place as the federated MFCS'98/CSL'98 conference and care will be taken that participants of the workshop can attend invited talks of the MFCS and CSL conferences. No special registration fee is required for participants who also register for MFCS'98 or CSL'98 and have a presentation at the workshop. Other workshop participants registered for MFCS'98 or CSL'98 will be requested to pay a small fee for the preliminary proceedings. Registration only for the workshop is also possible--expenses for fee, accommodation, and basic meals are very modest. Registration information can be found on the MFCS web page at http://www.fi.muni.cz/mfcs98. Organising Committee: L. Bernatsky (Szeged) A. Kucera (Brno) T. Szeles (Szeged) More information is available at the following web sites: http://www.inf.u-szeged.hu/fics/ http://www.cs.stevens-tech.edu/CFP/FICS/ From cat-dist Mon May 18 23:27:14 1998 Received: (from Majordom@localhost) by mailserv.mta.ca (8.8.8/8.8.8) id WAA03211 for categories-list; Mon, 18 May 1998 22:38:50 -0300 (ADT) X-Authentication-Warning: mailserv.mta.ca: Majordom set sender to cat-dist@mta.ca using -f X-Received: from inf.u-szeged.hu (csilla.inf.u-szeged.hu [160.114.37.74]) by mailserv.mta.ca (8.8.8/8.8.8) with SMTP id LAA15395 for ; Tue, 12 May 1998 11:10:21 -0300 (ADT) From: esik@inf.u-szeged.hu Message-Id: <199805121410.LAA15395@mailserv.mta.ca> Date: Tue, 12 May 98 16:09 MET To: rrosebrugh@mta.ca Sender: cat-dist@mta.ca Precedence: bulk Status: RO X-Status: >From esik Tue May 12 16:09:55 +0200 1998 remote from inf.u-szeged.hu To: rrosebrugh@mta.ca cc: esik Subject: FICS 2nd announcement Date: Tue, 12 May 1998 16:09:55 +0200 From: Esik Zoltan Received: from inf.u-szeged.hu by inf.u-szeged.hu; Tue, 12 May 1998 16:09 MET Content-Type: text Content-Length: 4630 Dear Professor Rosebrugh, Would you please forward the attached 2nd announcement of the FICS workshop to the subsribers of categories. Thank you in advance. Yours sincerely, Zoltan Esik ******************************************************************************* ******************************************************************************* ** ** ** F I C S ' 9 8 ** ** ** ** Fixed Points in Computer Science ** ** ** ** A Satellite Workshop to MFCS'98 ** ** ** ** August 27-28, 1998, Brno, Czech Republic ** ** ** ** Second Announcement ** ** ** ******************************************************************************* ******************************************************************************* Aim: Fixed points play a fundamental role in several areas of computer science, and the construction and properties of fixed points have been investigated in many different frameworks. The aim of the workshop is to provide a forum for researchers to present their results to those members of the computer science community who study or apply the fixed point operation in the different fields and formalisms. Topics: Construction and reasoning about properties of fixed points, categorical, metric and ordered fixed point models, continuous algebras, relation algebras, fixed points in process algebras and process calculi, regular algebra of finitary and infinitary languages, formal power series, tree automata and tree languages, infinite trees, the mu-calculus and other programming logics, fixed points in relation to dataflow and circuits, fixed points and the lambda calculus. Invited lectures: A. Arnold (Bordeaux): Boolean mu-calculus and its relations with model-checking and games J. W. de Bakker (Amsterdam): Fixed points in metric semantics Y. N. Moschovakis (Los Angeles/Athens): Fair, non-deterministic recursion in higher types (tentative) Program Committee: R. Backhouse (Eindhoven) S. L. Bloom (Hoboken) C. Boehm (Rome) R. De Nicola (Florence) Z. Esik (Szeged, chairman) P. Freyd (Philadelphia) I. Guessarian (Paris) D. Kozen (Cornell) W. Kuich (Vienna) M. Mislove (Tulane) R. F. C. Walters (Sydney) Contact person: Zoltan Esik Dept. of Computer Science Jozsef Attila University P.O.B. 652 6701 Szeged, Hungary e-mail: fics@inf.u-szeged.hu phone: ++36-62-454-289 fax: ++36-62-312-292 Paper submission: Authors are invited to send three copies of an abstract not exceeding three pages to the PC chair. Electronic submissions in the form of uuencoded postscript file are encouraged and can be sent to fics@inf.u-szeged.hu. Submissions are to be received before May 25, 1998. Authors will be notified of acceptance by June 25, 1998. Proceedings: Preliminary proceedings containing the abstracts of the talks will be available at the meeting. Publication of final proceedings as a special issue of Theoretical Informatics and Applications depends on the number and quality of the papers. The workshop will be organised at the same place as the federated MFCS'98/CSL'98 conference and care will be taken that participants of the workshop can attend invited talks of the MFCS and CSL conferences. No special registration fee is required for participants who also register for MFCS'98 or CSL'98 and have a presentation at the workshop. Other workshop participants registered for MFCS'98 or CSL'98 will be requested to pay a small fee for the preliminary proceedings. Registration only for the workshop is also possible--expenses for fee, accommodation, and basic meals are very modest. Registration information can be found on the MFCS web page at http://www.fi.muni.cz/mfcs98. Organising Committee: L. Bernatsky (Szeged) A. Kucera (Brno) T. Szeles (Szeged) More information is available at the following web sites: http://www.inf.u-szeged.hu/fics/ http://www.cs.stevens-tech.edu/CFP/FICS/ From cat-dist Tue May 19 17:40:00 1998 Received: (from Majordom@localhost) by mailserv.mta.ca (8.8.8/8.8.8) id QAA31374 for categories-list; Tue, 19 May 1998 16:17:00 -0300 (ADT) X-Authentication-Warning: mailserv.mta.ca: Majordom set sender to cat-dist@mta.ca using -f Date: Tue, 19 May 1998 18:34:33 +0100 Message-Id: <1525.199805191734@ling.dcs.ed.ac.uk> To: pareigis@math02.mathematik.uni-muenchen.de CC: categories@mta.ca In-reply-to: <9805170659.AB08536@math02> (pareigis@math02.mathematik.uni-muenchen.de) Subject: Re: categories: Who said: General Abstract Nonsense From: "Tim Heap" Sender: cat-dist@mta.ca Precedence: bulk Status: RO X-Status: pareigis writes: Bodo> Hi - who coined the expression Bodo> General Abstract Nonsense Bodo> as a synonym for category theory? Where did it first appear in Bodo> print? Lang, in his book `Algebra' says: "The terminology is due to Steenrod." tim From cat-dist Tue May 19 18:08:46 1998 Received: (from Majordom@localhost) by mailserv.mta.ca (8.8.8/8.8.8) id RAA01512 for categories-list; Tue, 19 May 1998 17:19:48 -0300 (ADT) X-Authentication-Warning: mailserv.mta.ca: Majordom set sender to cat-dist@mta.ca using -f X-Received: from uts.univ.trieste.it (uts.univ.trieste.it [140.105.48.16]) by mailserv.mta.ca (8.8.8/8.8.8) with ESMTP id MAA23314 for ; Mon, 18 May 1998 12:32:53 -0300 (ADT) X-Received: (from pedicchi@localhost) by uts.univ.trieste.it (8.8.8/8.8.8) id RAA13228; Mon, 18 May 1998 17:32:18 +0200 (MET DST) Date: Mon, 18 May 1998 17:32:18 +0200 (MET DST) From: "Pedicchio M. Cristina" To: Bob Rosebrugh Subject: categories: Informal seminar: Trieste In-Reply-To: Message-ID: MIME-Version: 1.0 Content-Type: TEXT/PLAIN; charset=US-ASCII Sender: cat-dist@mta.ca Precedence: bulk Status: RO X-Status: Bill Lawvere will be in Italy in July 98, so I am planning to organize an informal Seminar on the 10-11 of July in Trieste. A few European colleagues have already announced their participation; I welcome all interested people to participate. Please contact me by e-mail at the address pedicchi@univ.trieste.it M.Cristina Pedicchio" From cat-dist Tue May 19 21:28:19 1998 Received: (from Majordom@localhost) by mailserv.mta.ca (8.8.8/8.8.8) id UAA05269 for categories-list; Tue, 19 May 1998 20:42:56 -0300 (ADT) X-Authentication-Warning: triples.math.mcgill.ca: barr owned process doing -bs Date: Tue, 19 May 1998 18:43:26 -0400 (EDT) From: Michael Barr To: Tim Heap cc: pareigis@math02.mathematik.uni-muenchen.de, categories@mta.ca Subject: categories: Re: Who said: General Abstract Nonsense In-Reply-To: <1525.199805191734@ling.dcs.ed.ac.uk> Message-ID: MIME-Version: 1.0 Content-Type: TEXT/PLAIN; charset=US-ASCII Sender: cat-dist@mta.ca Precedence: bulk Status: O X-Status: This is interesting if indeed it was due to Steenrod. In that case, it was certainly not intended as a putdown (as Lang clearly intended it). Sammy Eilenberg told on a number of occasions the story that when General Theory of Natural Equivalences was published, Steenrod said that no paper had ever influenced his thinking more. He had been searching for years for an axiomatization of homology theory, but had never thought of using the induced homomorphisms as the basic tool. The result was, of course, the Eilenberg-Steenrod axioms. (The rest of the story is that P.A. Smith said he never read a more trivial paper in his life. Sammy commented that both reactions were valid.) On Tue, 19 May 1998, Tim Heap wrote: > pareigis writes: > > Bodo> Hi - who coined the expression > Bodo> General Abstract Nonsense > Bodo> as a synonym for category theory? Where did it first appear in > Bodo> print? > > Lang, in his book `Algebra' says: > "The terminology is due to Steenrod." > > tim > From cat-dist Wed May 20 12:26:14 1998 Received: (from Majordom@localhost) by mailserv.mta.ca (8.8.8/8.8.8) id JAA15623 for categories-list; Wed, 20 May 1998 09:08:23 -0300 (ADT) X-Authentication-Warning: mailserv.mta.ca: Majordom set sender to cat-dist@mta.ca using -f X-Sender: duskin@buffnet.net Message-Id: Mime-Version: 1.0 Content-Type: text/enriched; charset="us-ascii" Date: Tue, 19 May 1998 20:16:08 -0400 To: categories@mta.ca From: John Duskin Subject: categories: Nonsense Sender: cat-dist@mta.ca Precedence: bulk Status: O X-Status: It might be amusing for people to see the full context as I replied to Bodo: Serge Lang used it in his Addiison-Wesley text: " Algebra" in the first(?) 1965 edition. On page 105 after the chapter on Homology, the following appears: "EXERCISES: Take any book on homological algebra, and prove all the theorems without looking at the proofs given in that book. Homological algebra was invented by Eilenberg-Mac Lane. General category theory (i.e. the theory of arrow-theoretic results ) is generally known as abstract nonsense ( the terminology is due to Steenrod)." From cat-dist Wed May 20 12:26:22 1998 Received: (from Majordom@localhost) by mailserv.mta.ca (8.8.8/8.8.8) id JAA16288 for categories-list; Wed, 20 May 1998 09:11:39 -0300 (ADT) X-Authentication-Warning: mailserv.mta.ca: Majordom set sender to cat-dist@mta.ca using -f Date: Wed, 20 May 1998 12:46:09 +1000 (EST) From: Sjoerd Erik CRANS Message-Id: <199805200246.MAA24685@krakatoa.mpce.mq.edu.au> To: categories@mta.ca Subject: categories: Re: question about omega-category Cc: gaucher@irma.u-strasbg.fr, scrans@krakatoa.mpce.mq.edu.au X-Sun-Charset: US-ASCII Sender: cat-dist@mta.ca Precedence: bulk Status: O X-Status: Philippe Gaucher wrote: > Dear categorician (or categorist, I do not know the word in English), > > > I posted the following question some days ago in sci.math.research. > Maybe this list is more appropirated : > > I would need to understand a proof of the following proposition : > > There is only one functor up to isomorphism TENS : omega-Cat x > omega-Cat -> omega-Cat for which C TENS - and - TENS C have right > adjoint for every omega-category C and which satisfies I^p TENS I^q = > I^{p+q} where I^p is the omega-category canonically associated to the > p-cube, (using for example the set of composable sub pasting schemes > of the pasting scheme associated to the p-cube). > > I have a paper from Crans ("Pasting schemes for the monoidal biclosed > structure on omega-Cat") which proves explicitely the proposition. I > do not understand the construction, which is very technical (*). Is there > a less complicated way to prove this proposition ? I do not need an > explicit construction. > > Any help is welcome. > > pg. > > > (*) What is a pasting presentation for example ? I know the definition > of pasting scheme, realization of pasting schemes, but I do not know the > one of "pasting presentation". Another question : if f, g are morphisms > in C and h, k morphisms in D, is there in C TENS D elements corresponding > to f TENS h and g TENS k, and if the answer is yes, is it true that > (f TENS h) o_p (g TENS k) = (f o_p g) TENS (h o_p k) ? I suppose that > it is false : if it should be true, why the construction of this monoidal > structure is so complicated ? > A pasting presentation for an omega-category is similar to a presentation for a group, but taking into account that there are cells of different dimensions. In particular, generators in dimension n are ``labeled'' n-dimensional pasting schemes with the labeling involving generators *and relations* in lower dimensions. More details about pasting presentations can be found in my paper "Pasting presentations for omega-categories", which is available via my web-page: http://www.mpce.mq.edu.au/~scrans/papers/ or via hypatia: http://hypatia.dcs.qmw.ac.uk/author/C/CransSE/. The proposition above follows by general categorical methods, using the adjunction between omega-categories and cubical sets. Apart from my proof cited above there are earlier proofs by Al-Agl and Steiner [Nerves of multiple categories, Proc. London Math. Soc. (3) 66 (1993) 92-128] and by Brown and Higgins [Tensor products and homotopies for omega-groupoids and crossed complexes] (who only do omega-groupoids but their proof holds for omega-categories as well). Yes, there are elements in C TENS D corresponding to f TENS h and g TENS k. But is not just that (f TENS h) o_p (g TENS k) = (f o_p g) TENS (h o_p k) is not true: it does not even make sense, because the sources and targets don't match up. Sjoerd Crans From cat-dist Wed May 20 12:27:19 1998 Received: (from Majordom@localhost) by mailserv.mta.ca (8.8.8/8.8.8) id JAA12537 for categories-list; Wed, 20 May 1998 09:13:46 -0300 (ADT) X-Authentication-Warning: mailserv.mta.ca: Majordom set sender to cat-dist@mta.ca using -f X-Received: from motgate.mot.com (motgate.mot.com [129.188.136.100]) by mailserv.mta.ca (8.8.8/8.8.8) with ESMTP id VAA01100 for ; Tue, 19 May 1998 21:46:16 -0300 (ADT) X-Received: from pobox.mot.com (pobox.mot.com [129.188.137.100]) by motgate.mot.com (8.8.5/8.6.10/MOT-3.8) with ESMTP id TAA02927; Tue, 19 May 1998 19:44:12 -0500 (CDT) Comments: ( Received on motgate.mot.com from client pobox.mot.com, sender peter@galois.geg.mot.com ) X-Received: from motgeg.geg.mot.com (motgeg.geg.mot.com [192.88.158.100]) by pobox.mot.com (8.8.5/8.6.10/MOT-3.8) with SMTP id TAA27030; Tue, 19 May 1998 19:44:11 -0500 (CDT) X-Received: from opus-tr.geg.mot.com by motgeg.geg.mot.com (AIX 4.1/UCB 5.64/4.03) id AA26502; Tue, 19 May 1998 18:42:30 -0500 X-Received: by galois.geg.mot.com (SMI-8.6/SMI-SVR4) id RAA07137; Tue, 19 May 1998 17:30:31 -0700 Date: Tue, 19 May 1998 17:30:31 -0700 From: peter@galois.geg.mot.com (Peter White) Message-Id: <199805200030.RAA07137@galois.geg.mot.com> To: barr@math.mcgill.ca Subject: categories: Re: Who said: General Abstract Nonsense Cc: cat-dist@mta.ca X-Sun-Charset: US-ASCII Sender: cat-dist@mta.ca Precedence: bulk Status: O X-Status: A quote from a Colin McLarty posting on another list: " Norman Steenrod first hung this tag on category theory. He had spent years trying to axiomatize homology, encouraged by Solomon Lefschetz. Lefschetz had also backed the young topologist Sammy Eilenberg, and encouraged Eilenberg's collaboration with the algebraist Mac Lane explicating certain calculations in homology. When Eilenberg and Mac Lane created category theory, Steenrod saw he could use their way of emphasizing morphisms at least as much as objects. He happily said this "abstract nonsense" was the key to solving his problem. The phrase was popularized by Lang's ALGEBRA, which had an index entry under "abstract nonsense". The page numbers sent you to various one line proofs such as "By abstract nonsense, tensor products are unique up to isomorphism when they exist". The joke got old and survives only vestigially in the latest edition." Peter White On Tue, May 19th, Michael Barr wrote: > > This is interesting if indeed it was due to Steenrod. In that case, it > was certainly not intended as a putdown (as Lang clearly intended it). > Sammy Eilenberg told on a number of occasions the story that when General > Theory of Natural Equivalences was published, Steenrod said that no paper > had ever influenced his thinking more. He had been searching for years > for an axiomatization of homology theory, but had never thought of using > the induced homomorphisms as the basic tool. The result was, of course, > the Eilenberg-Steenrod axioms. (The rest of the story is that P.A. Smith > said he never read a more trivial paper in his life. Sammy commented that > both reactions were valid.) > From cat-dist Thu May 21 13:00:00 1998 Received: (from Majordom@localhost) by mailserv.mta.ca (8.8.8/8.8.8) id KAA05391 for categories-list; Thu, 21 May 1998 10:10:50 -0300 (ADT) X-Authentication-Warning: triples.math.mcgill.ca: barr owned process doing -bs Date: Thu, 21 May 1998 08:44:12 -0400 (EDT) From: Michael Barr To: Categories list Subject: categories: Regular embedding Message-ID: MIME-Version: 1.0 Content-Type: TEXT/PLAIN; charset=US-ASCII Sender: cat-dist@mta.ca Precedence: bulk Status: RO X-Status: A month or so ago, I got a note from Ross Street asking about my 1986 JPAA paper on representations of categories. The main point of that paper was to give a new, relatively simple proof of the full embedding theorem for regular categories. Unfortunately, I tried to get too general and got tangled in the variance, so that the argument could not be followed. Follows is my final note to Ross. The argument is really quite simple and can be described as follows: 1. Show that when @C (read script C) is regular, so is Lex(@C,Set)\op. (Lex=FL is the finite limit preserving functors. This result is really the only new thing in the paper.) 2. Adapt Grothendieck's transfinite induction proof of the existence of injectives in an AB5 abelian category to show that Lex(@C,Set)\op has enough @C-projectives = regular functors. 3. Adapt Mitchell's proof of the abelian category full embedding theorem to show that by taking a sufficiently large full subcategory @P in Lex(@C,Set) consisting of regular functors, then the evaluation functor @C --> Func(@P\op,Set) is full and faithful. That's all there is to it. I plan to post on triples in the next few days a revised version of the paper (it was, fortunately, one of the very first that was typed on a computer, so this is not too onerous). I will call it embedding.rev. Ross further raised the question as to whether a transfinite induction was too sophisticated for the classroom. I don't know exactly what level his course was, but I will say that if we never do a hard theorem, then the students will come away with the idea that there is no depth to category theory, an impression his colleagues will be only too happy to affirm. This argument of Grothendieck's is, after all, the first example that there could be deep results in categories. Michael ===================================================================== Dear Ross: I did not really try to understand my paper. I suspect it is a matter of trying to be too abstract and getting tangled in my own feet. At any rate, here is how I would do it for a class. First, since you didn't ask, I assume that you are happy with the fact that given a small category @C (think of that as script C; BTW, I never noticed how dreadful JPAA's scripts were), the category @L = Lex(@C,Set)\op has the property that given any functor F, there is a regular epi P -->> F such that P is projective with respect to regular epis in @C. Now consider a small full subcategory @P built out of choosing @C projective covers for each representable and a @C-projective cover for the kernel pair of each of the @C-projective covers of representables. Thus, for each object C, there is a parallel pair Q ===> P in @P, whose coequalizer in @L is C. Notice that Hom_{@L}(P,C) = PC, using Yoneda and taking the variance into account. There is an obvious functor F: @C --> Fun(@P\op,Set) that takes C to the functor P |--> Hom(P,C) = PC. This functor is clearly faithful, preserves finite limits and regular epis. The only question is the fullness. So suppose a: FC --> FB is a natural transformation. What naturality means is that for any d: Q --> P in @P, the square Hom(d,C) Hom(P,C) ----------> Hom(Q,C) | | | | aP | | aQ | | | | v v Hom(P,B) ----------> Hom(Q,B) Hom(d,B) commutes. Applied to an f: P --> C, this means that aQ(d.f) = d.aP(f). Apply this in the case that f is a coequalizer in @L to a parallel pair d,e : Q ===> P in @P. It says that aP(f).d = aQ(f.d) = aQ(f.e) = aQ(f).e and that means that there is a unique b: C --> B such that aP(f) = b.f. You finish the argument by observing that for any object R of @P and any c: R --> C, there is a lifting to an arrow g: R --> P and then aR(c) = aR(f.g) = aP(f).g = b.f.g = b.c. From cat-dist Thu May 21 14:52:27 1998 Received: (from Majordom@localhost) by mailserv.mta.ca (8.8.8/8.8.8) id NAA25584 for categories-list; Thu, 21 May 1998 13:16:08 -0300 (ADT) X-Authentication-Warning: mailserv.mta.ca: Majordom set sender to cat-dist@mta.ca using -f Message-ID: <3561D489.87EAB0F1@brandx.net> Date: Tue, 19 May 1998 14:50:49 -0400 From: Zhaohua Luo X-Mailer: Mozilla 4.05 [en] (Win95; I) MIME-Version: 1.0 To: categories@mta.ca Subject: categories: abstract algebraic geometry Content-Type: text/plain; charset=us-ascii Content-Transfer-Encoding: 7bit Sender: cat-dist@mta.ca Precedence: bulk Status: O X-Status: The following paper Categorical Geometry: 2 Analytic Topologies is available on my WWW home page at the following new address: http://modigliani.brandx.net/user/zluo/ (the old address will soon cease to work). Regards, Zack Luo From cat-dist Thu May 21 15:18:31 1998 Received: (from Majordom@localhost) by mailserv.mta.ca (8.8.8/8.8.8) id NAA29259 for categories-list; Thu, 21 May 1998 13:23:13 -0300 (ADT) X-Authentication-Warning: mailserv.mta.ca: Majordom set sender to cat-dist@mta.ca using -f MIME-Version: 1.0 Content-Type: text/plain; charset=us-ascii Content-Transfer-Encoding: 7bit Date: Wed, 20 May 1998 15:59:42 +0200 (MET DST) From: Davide Sangiorgi To: concurrency@cwi.nl, categories@mta.ca, logic@CS.Cornell.EDU, types@cs.indiana.edu, THEORYNT@LISTSERV.NODAK.EDU Subject: categories: CONCUR '98: ACCEPTED PAPERS (and general infos) CC: Robert.De_Simone@sophia.inria.fr, Davide.Sangiorgi@sophia.inria.fr X-Mailer: VM 6.43 under 20.4 "Emerald" XEmacs Lucid Message-ID: <13666.57201.904572.333575@pancia.inria.fr> Sender: cat-dist@mta.ca Precedence: bulk Status: O X-Status: CONCUR'98 9th International Conference on Concurrency Theory Nice, France, September 8-11, 1998 ******************************************************************* Please find below the list of PAPERS ACCEPTED at CONCUR 98, and other information including INVITED SPEAKERS and TUTORIALS, SATELLITE EVENTS, VENUE, and SOCIAL PROGRAMME. ******************************************************************** List of Accepted Papers (ordered by submission number) ~~~~~~~~~~~~~~~~~~~~~~~ Deriving unbounded Petri nets from formal languages by Philippe Darondeau Synthesis of ENI-systems Using Minimal Regions by Marta Pietkiewicz-Koutny Unfolding and Finite Prefix for Nets with Read Arcs by W. Fogler, A. Semenov, A. Yakovlev Reduction in TLA by Ernie Cohen, Leslie Lamport Herbrand Automata for Hardware Verification by W. Damm, A. Pnueli, S. Ruah Asynchronous and asynchronous cellular automata for pomsets by Dietrich Kuske A categorical axiomatics for bisimulation by Gian Luca Cattani, John Power, Glynn Winskel Priority and Maximal Progress are completely axiomatisable by Holger Hermanns, Markus Lohrey Modelling IP Mobility by Roberto M. Amadio, Sanjiva Prasad Synthesis from Knowledge-Based Specifications by Ron van der Meyden, Moshe Y. Vardi Stochastic Transition Systems by Luca de Alfaro Minimality and Separation Results on Asynchronous Mobile Processes: representability theorem by concurrent combinators by Nobuko Yoshida Reasoning about asynchronous communication in dynamically evolving object structures. by F.S. de Boer >From Rewrite Rules to Bisimulation Congruences by Peter Sewell Detecting Deadlocks in Concurrent Systems by Lisbeth Fajstrup, Eric Goubault, Martin Raussen The Tau-Laws of Fusion by Joachim Parrow, Bjorn Victor Algebraic techniques for timed systems by A. Benveniste, C. Jard, S. Gaubert Control Flow Analysis for the pi-calculus by Chiara Bodei, Pierpaolo Degano, Flemming Nielson, Hanne Riis Nielson Simulation is Decidable for One-counter Nets by Parosh Aziz Abdulla, Karlis Cerans Fibrational Semantics of Dataflow Networks by Eugene W. Stark >From Higher-Order pi-Calculus to pi-Calculus in the Presence of Static Operators by Jose-Luis Vivas, Mads Dam Axioms for Real-Time Logics by Jean-Francois Raskin, Pierre-Yves Schobbens, Tom Henzinger Unfold/Fold Transformations of CCP programs by Sandro Etalle, Maurizio Gabbrielli, Maria Chiara Meo A Relational Model of Non-Deterministic Dataflow by Thomas Hildebrandt, Prakash Panangaden, Glynn Winskel Decompositions of Asynchronous Systems by Remi Morin Controlled Timed Automata by Francois Demichelis, Wieslaw Zielonka Abstract games for infinite-state processes by Perdita Stevens Alternating Simulation by R. Alur, T. Henzinger, O. Kupferman On Discretization of Delays in Timed Automata and Digital Circuits by Eugene Asarin, Oded Maler, Amir Pnueli Partial Order Reductions for Timed Systems by Johan Bengtsson, Bengt Jonsson, Johan Lilius, Wang Yi Controllers for Discrete Event Systems via Morphisms by P Madhusudan, P S Thiagarajan The Regular Viewpoint on PA-Processes by D. Lugiez, Ph. Schnoebelen Probabilistic Resource Failures in Real-Time Process Algebra by Anna Philippou, Oleg Sokolsky, Insup Lee, Rance Cleaveland, and Scott Smolka Possible Worlds for process algebras by Simone Veglioni, Rocco de Nicola Towards Performance Evaluation with General Distributions in Process Algebras by Mario Bravetti, Marco Bernardo, Roberto Gorrieri Invited Speakers and Tutorials: ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ (in square brackets, the topic of the talk) Invited Speakers: T. Henzinger (University of California at Berkeley, USA) [Hybrid systems]; U. Herzog (Erlangen, Germany) [Process algebra for performance evaluation]; J. Rutten (CWI, Netherlands) [Coalgebraic models of computation]; J.-B. Stefani (CNET, France Telecom) [Open distributed systems]; M. Vardi (Rice University, USA) [Branching and linear time temporal logics]. Invited Tutorials : G. Berry (CMA Ecole des Mines, France) [Synchronous reactive programming and Esterel]; J.F. Groote (CWI, Netherlands) [Theorem provers in concurrency]; B. Pierce (Indiana U., USA) [Types in concurrency]. Satellite events ~~~~~~~~~~~~~~~~~ COTIC'98: 2nd international workshop on Concurrent Constraint Programming for Time Critical Applications EXPRESS'98: 5th international workshop on Expressiveness in Concurrency HLCL'98: 3rd international workshop on High-Level Concurrent Languages PAPM'98: 6th international workshop on Process Algebra and Performance Modeling CONFER W.G.: 4th workshop of the CONFER (Concurrency and Functions: Evaluation and Reduction) working group. Watch out: Submission deadlines for COTIC'98, EXPRESS'98, HLCL'98, PAPM'98 are coming up! Participation to COTIC'98, EXPRESS'98 and HLCL'98 will require no fees; PAPM will require a (low) fee; participation to CONFER is by invitation. Venue and local arrangements ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ Nice is ideally located on the French Riviera. September is still very pleasant, while less crowded than the high season. Nice's international airport is well-connected to all major european and non-european cities. The conference will be held at the auditorium of Nice Museum of Modern and Contemporary Art, which is conveniently located in the heart of Nice, between the city center and the old town, and 20 minutes walk to the beach. The Museum is next to the Hotel Novotel, where tutorials, satellite workshops, and registration will be held. Social programme (to be confirmed) ~~~~~~~~~~~~~~~~ - cocktail offered by the City of Nice at the Modern Art Museum Cafe. - excursion at Cap Ferrat on Thursday 10. Cap Ferrat is a beautiful promontory between Nice and Monaco. Its attractions include: walks with spectacular views of the coast, beaches, Villa Kerylos (a copy of a sumptuous antique Greek house), Ephrussi de Rothchild Foundation, the charming villages of St-Jean-Cap-Ferrat and Beaulieu-sur-Mer. - banquet on Thursday 10 (evening) at the Royal Riviera Hotel of St-Jean-Cap-Ferrat (one of the coast's most stylish establishments). Registration and hotel information ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ Both the hotel and the registration information will be available from June 8th at the CONCUR web page. ============================= For further information, check URL , or mail to concur98@sophia.inria.fr. From cat-dist Fri May 22 11:46:33 1998 Received: (from Majordom@localhost) by mailserv.mta.ca (8.8.8/8.8.8) id JAA18316 for categories-list; Fri, 22 May 1998 09:10:22 -0300 (ADT) X-Authentication-Warning: mailserv.mta.ca: Majordom set sender to cat-dist@mta.ca using -f Message-Id: <199805220404.OAA16416@macadam.mpce.mq.edu.au> X-Sender: street@macadam.mpce.mq.edu.au Mime-Version: 1.0 Content-Type: text/plain; charset="us-ascii" Date: Fri, 22 May 1998 14:05:30 +1000 To: categories@mta.ca From: street@mpce.mq.edu.au (Ross Street) Subject: categories: Re: Regular embedding Sender: cat-dist@mta.ca Precedence: bulk Status: O X-Status: The proof Michael Barr had in mind at the time of writing his 1986 JPAA paper on representations of categories, and has now clarified, is truly beautiful. I may have misrepresented what the problem was with presenting the transfinite induction part of the proof in my course. It is a question of time rather than difficulty. I am not known amongst my colleagues as one who shrinks from teaching or avoiding hard proofs. The point is that I have a course consisting of 24 lectures to a group including a (bright) 4th year student (who had hardly heard of categories before the course), a graduate students in number theory, physics and computer science, my own 5 PhD students, and a professional category theorist. I am trying to keep it interesting for all. The students (even the ones who have done a formal set-theory course) have not really used ordinals; so I would need to sacrifice some category theory to provide that background. I am still undecided about this; perhaps, the transfinite induction and the embedding theorem can be an appendix to the course. Perhaps the most novel aspect of the course, considering my 2-cell background, is that I have given 18 lectures so far without introducing natural transformations. I'm about to talk about adjunctions without them too. I must admit that the course content has evolved on the run. But looking back, I think it has some unity of purpose. I headed straight for the definition of regular category as having a terminal object, pullbacks, strong epi - monic factorizations, and stability of strong epis under pulling back along arbitrary arrows. We developed the method of generalised elements and constructed the Poset-enriched category of relations in a regular category. We proved relations with right adjoints are graphs of arrows. We proved strong epis are regular. Equivalence relations and (Barr-)exact categories were examined. [One of my (intended?) questions to Michael Barr was whether he knew of a diagram lemma which could be proved significantly quicker using the embedding theorem than by the generalised-element/relations technology.] I proved in detail that an exact additive category is abelian (as defined in Freyd's book "Abelian Categories" - beginning of Chapter 2). Not only is that a deep theorem of category theory (in my opinion - despite not needing a transfinite argument) but it is a microcosm of categorical ideas that have proved useful in other contexts. We proved the Five Lemma, Snake Lemma using relations in the abelian category. So far I have set 15 exercises: some quite challenging. One was to prove Cat is not regular (I gave a bit of a hint). Now I am discussing 2-sided discrete fibrations (just for categories) in depth. These are being advertised as the "relations" of category theory. In fact, this means we do have presheaf categories disguised as DFib(A,1); so some natural transformations are there hiding there. I have this weekend to decide where we go next! But I think there is enough meat in all this to deal with sceptical colleagues. When it comes to a game of "my subject's harder than yours, nya, nya", I would also argue that the concepts category theory has to offer are just as hard to really master as difficult theorems. This is why many mathematicians calculate hard to do what we can do with our concepts. Regards, Ross From cat-dist Fri May 22 15:36:39 1998 Received: (from Majordom@localhost) by mailserv.mta.ca (8.8.8/8.8.8) id OAA31857 for categories-list; Fri, 22 May 1998 14:31:09 -0300 (ADT) X-Authentication-Warning: triples.math.mcgill.ca: barr owned process doing -bs Date: Fri, 22 May 1998 11:25:25 -0400 (EDT) From: Michael Barr To: Ross Street cc: categories@mta.ca Subject: categories: Re: Regular embedding In-Reply-To: <199805220404.OAA16416@macadam.mpce.mq.edu.au> Message-ID: MIME-Version: 1.0 Content-Type: TEXT/PLAIN; charset=US-ASCII Sender: cat-dist@mta.ca Precedence: bulk Status: O X-Status: I certainly welcome Ross' clarification of his problem. One possibility would be to give the proof except for the existence of sufficient regular functors and either refer the students to the paper or (better) write it out carefully and distribute it. One thing I have given only a little thought to is whether it can be done using a maximal principle argument. The point is that it is not a question of extending a map to a larger and larger subobject, but of building larger and larger objects and not as subobjects of something already given. This makes it different from the proof, say, that divisible abelian groups are injective (from which the existence of sufficient injectives in any module category follows easily). I think a maximal principle argument goes down a lot more easily than one based overtly on ordinals or transfinite induction. Ross, it sounds like a beautiful course and if you have notes, I would like to see them. Michael From cat-dist Fri May 22 15:40:19 1998 Received: (from Majordom@localhost) by mailserv.mta.ca (8.8.8/8.8.8) id OAA01824 for categories-list; Fri, 22 May 1998 14:30:16 -0300 (ADT) X-Authentication-Warning: mailserv.mta.ca: Majordom set sender to cat-dist@mta.ca using -f Date: Fri, 22 May 1998 15:00:05 +0100 (BST) From: Paul Taylor Message-Id: <199805221400.PAA08998@ruby.dcs.qmw.ac.uk> To: categories@mta.ca Subject: categories: "Practical Foundations of Mathematics" Sender: cat-dist@mta.ca Precedence: bulk Status: O X-Status: Practical Foundations of Mathematics, ISBN 0-521-63107-6 To be published by Cambridge University Press, as number 59 in their series Cambridge Studies in Advanced Mathematics (which includes books by Peter Johnstone and by Jim Lambek and Phil Scott). Please see http://www.dcs.qmw.ac.uk/~pt/book/index.html for details. This is the LAST CALL FOR COMMENTS. The text is already in the hands of the copy editor for the second time. CUP hopes to have it published in time for the International Congress of Mathematicians in Berlin in August, which means I have to finish it by the end of May. I am aware that my policy of only giving away single chapters has annoyed people a bit, but it has been successful in its objective of getting attention for the whole book. (The most assiduous reader of "Proofs and Types" got to chapter 12 out of 15). I don't intend to distribute any more chapters now, though if I owe you a copy of the whole draft because you sent me comments on a chapter, please ask (tearing apart sections 1.1 and 1.2 does not count). If you have a copy of part of the book and have noticed a mis-conception, please SPEAK NOW OR FOREVER HOLD YOUR PEACE. There is really no point in telling me about missing commas in any but the most recent versions (ie 1998) as other readers, the copy editor and I have been through the text several times since I last distributed copies (in July 1997). When I am rid of the book itself, I intend to set up a web site as a repository for citations, discussion, answers to exercises and, inevitably, corrections. With the permission of the people concerned, I intend to publish some of the correspondence I have had about the book in this way, and there will be automatic facilities for readers to add further comments. Therefore any comments you have about the book which are too late for publication or which are not suitable for inclusion will not be wasted. I would like thank Pierre Ageron, Lars Birkedal, Luca Cattani, Michel Chaudron, Thierry Coquand, Robert Dawson, Luis Dominguez, Peter Dybjer, Susan Eisenbach, Fabio Gadducci, Gillian Hill, Martin Hyland, Samin Ishtiaq, Achim Jung, Stefan Kahrs, J\"urgen Koslowski, Steve Lack, Jim Lambek, Charles Matthews, Paddy Mccrudden, James Molony, Edmund Robinson, Pino Rosolini, Martin Sadler, Alan Sexton, Thomas Streicher, Charles Wells, Graham White, Andrew Wilson and Todd Wilson for taking the trouble to read parts of the draft and giving their detailed comments on it. (Please tell me if you think you should be on this list but aren't.) Paul Taylor From cat-dist Fri May 22 18:33:58 1998 Received: (from Majordom@localhost) by mailserv.mta.ca (8.8.8/8.8.8) id RAA07992 for categories-list; Fri, 22 May 1998 17:36:32 -0300 (ADT) X-Authentication-Warning: mailserv.mta.ca: Majordom set sender to cat-dist@mta.ca using -f X-Received: from hopper.unh.edu (dv@hopper.unh.edu [132.177.137.8]) by mailserv.mta.ca (8.8.8/8.8.8) with ESMTP id OAA32216 for ; Fri, 22 May 1998 14:31:54 -0300 (ADT) X-Received: (from dv@localhost) by hopper.unh.edu (8.8.8/8.8.8) id NAA16879; Fri, 22 May 1998 13:31:52 -0400 (EDT) Date: Fri, 22 May 1998 13:31:52 -0400 (EDT) Message-Id: <199805221731.NAA16879@hopper.unh.edu> From: Donovan Van Osdol To: rrosebrugh@mta.ca Subject: categories: Re: Regular embedding Sender: cat-dist@mta.ca Precedence: bulk Status: O X-Status: Ross Street asks Michael Barr if he knows "of a diagram lemma which could be proved significantly quicker using the embedding theorem than by the generalized-element/relations technology". Well, I don't exactly, but one of the earliest uses of Barr's embeddings of regular categories was in my American Journal of Mathematics paper on Simplicial Homotopy in an Exact Category (1977, vol 99, pp 1193-1204). I wanted to prove the homotopy exact sequence of a Kan fibration of sheaves of simplicial sets and Barr's results were exactly what I needed. All this has since been improved by using closed model structures and a less naive definition of fibration, but the "embedding/technology" Ross mentions was all we had available--in sufficient generality to cover my situation--at the time. Don Van Osdol From cat-dist Sun May 24 13:04:50 1998 Received: (from Majordom@localhost) by mailserv.mta.ca (8.8.8/8.8.8) id LAA32390 for categories-list; Sun, 24 May 1998 11:47:37 -0300 (ADT) X-Authentication-Warning: mailserv.mta.ca: Majordom set sender to cat-dist@mta.ca using -f Date: Sat, 23 May 1998 23:31:46 -0500 From: ralphw@math.uiuc.edu (Ralph Leonard Wojtowicz) Message-Id: <199805240431.XAA01753@ginger.math.uiuc.edu.math.uiuc.edu> To: categories@mta.ca Sender: cat-dist@mta.ca Precedence: bulk Status: RO X-Status: On pages 29--30 of "Categories for the Working Mathematician," MacLane reveals that "the discovery of ideas as general as [categories, functors and natural transformations] is chiefly the willingness to make a brash or speculative abstraction, in this case supported by the pleasure of purloining words from the philosophers: `Category' from Aristotle and Kant, `Functor' from Carnap and `natural transformation' from then current informal parlance." Ideas from writings of Karl Marx are described in "Conceptual Mathematics: A First Introduction to Category Theory," by Lawvere and Schanuel and elsewhere. What orientation or program of study has philosophy given the investigation of mathematical categories? Where could one begin reading to understand this influence? Was selection of "monad" influenced by writings of Leibniz? Thank you for your time. Sincerely, Ralph Wojtowicz From cat-dist Tue May 26 14:07:30 1998 Received: (from Majordom@localhost) by mailserv.mta.ca (8.8.8/8.8.8) id LAA22722 for categories-list; Tue, 26 May 1998 11:47:21 -0300 (ADT) X-Authentication-Warning: mailserv.mta.ca: Majordom set sender to cat-dist@mta.ca using -f Date: Mon, 25 May 1998 17:10:01 +0200 (MET DST) Message-Id: <199805251510.RAA21967@harald.daimi.aau.dk> From: Uffe Henrik Engberg To: categories@mta.ca Subject: categories: ICALP'98: 2nd Call for Participation Mime-Version: 1.0 (generated by tm-edit 7.106) Content-Type: text/plain; charset=ISO-8859-1 Content-Transfer-Encoding: 8bit Sender: cat-dist@mta.ca Precedence: bulk Status: RO X-Status: ---------------------------------------------------------------------- If you have already registered for ICALP98 please ignore this message! ---------------------------------------------------------------------- SECOND CALL FOR PARTICIPATION EXTENDED EARLY REGISTRATION: June 1st and NEW SPECIAL STUDENT REGISTRATION FEE ICALP'98 25th International Colloquium on Automata, Languages, and Programming Aalborg, Denmark July 13-17, 1998 http://www.cs.auc.dk/icalp98/ The International Colloquium on Automata, Languages, and Programming (ICALP) is the annual conference series of the European Association for Theoretical Computer Science (EATCS). It is intended to cover all important areas of theoretical computer science. During 5 conference days and two weekends, ICALP will give you the opportunity to choose between 70 regular papers, 9 invited lectures, including the Gödel award lecture, and 4 thematic workshops and one associated summer school offering dozens of more talks! Due to a recent General Strike in Denmark the ICALP booklet has been delayed. Therefore we extend the deadline for early registration to JUNE 1st The final deadline for registration is still June 12. Upon numerous requests student may now register at a special low fee (DKK 1200 before June 1 and DKK 1400 after). The fee will cover conference attendance, refreshments and lunches only. Proceedings and banquet tickets can be purchased separately on arrival. Students who have already registered at the regular fee may choose on arrival to receive a refund. The full programme and registration form are available at the web address above and from the organizers (just send a message to icalp98@cs.auc.dk or a fax to +45 98159889). Kim Guldstrand Larsen ICALP Conference chair BRICS Department of Computer Science Aalborg University Fredrik Bajersvej 7 9220 Aalborg DENMARK Tel.: +45 96 35 88 93 (direct) From cat-dist Tue May 26 14:13:08 1998 Received: (from Majordom@localhost) by mailserv.mta.ca (8.8.8/8.8.8) id MAA23844 for categories-list; Tue, 26 May 1998 12:11:41 -0300 (ADT) X-Authentication-Warning: mailserv.mta.ca: Majordom set sender to cat-dist@mta.ca using -f Date: Mon, 25 May 1998 17:00:07 -0400 Message-Id: <199805252100.RAA14212@triples.math.mcgill.ca> From: "Ockham's stubble" To: categories@mta.ca Subject: categories: Regular embedding Sender: cat-dist@mta.ca Precedence: bulk Status: RO X-Status: Would the following (aside from the first) help to prepare a more digestible proof of Barr's full regular embedding theorem? 1) Say that an object U of a (but not just any) category E is open if U is a finitely presentable object of the opposite of E (i.e., if it satisfies the analogue of the filter convergence characterization of open sets). An object P of E is strict if it is the projective limit of a diagram of opens such that each limit projection is an effective epimorphism; P is called saturated if for every U -->> V of opens, each P -->> V lifts to some P -->> U; finally, P is called weakly projective if it is projective with respect to effective epimorphisms of opens. Every strict, saturated object is weakly projective. 2) Given P in Pro(C), where C is a regular category, let P' denote the fibred product of all X -->> P which are opens of Pro(C)/P, and P* the projective limit of: P <<-- P' <<-- P'' <<-- P''' ...; one shows that the projection P* --> P is an effective epimoprhism, that P* is a strict, saturated object of Pro(C)/P, and therefore that P* is a weakly projective object of Pro(C). Theorem 14 of Barr's '86 JPAA paper (i.e., step three in his message of 21 May) applies. 3) The construction is (to my knowledge) due to Joyal (c. 1972, or earlier). Objects of the form X*, where X is an object of C, are principal prime models, a notion Makkai (Full continuous embeddings of toposes, Trans AMS, 1982) distilled from Barr's original proof (Joyal called them absolutely flasque). cheers, -b PS:Without the terminology, that Pro(C) (=~ Lex(C,Set)^op) is regular if C is is suggested in SGA4, Expose I, 8.9 (especially cf. exercise 8.9.9(b)). From cat-dist Tue May 26 21:25:31 1998 Received: (from Majordom@localhost) by mailserv.mta.ca (8.8.8/8.8.8) id TAA06693 for categories-list; Tue, 26 May 1998 19:29:43 -0300 (ADT) X-Authentication-Warning: triples.math.mcgill.ca: barr owned process doing -bs Date: Tue, 26 May 1998 14:03:07 -0400 (EDT) From: Michael Barr Reply-To: Michael Barr To: "Ockham's stubble" cc: categories@mta.ca Subject: Re: categories: Regular embedding In-Reply-To: <199805252100.RAA14212@triples.math.mcgill.ca> Message-ID: MIME-Version: 1.0 Content-Type: TEXT/PLAIN; charset=US-ASCII Sender: cat-dist@mta.ca Precedence: bulk Status: RO X-Status: Well, I am not trying to be snide, but for me, my argument is more understandable. But if you prefer to see it in the way you put it, I have no objection. A couple more comments. In 1986 (or, really, 1984), I did not really understand that this argument was *really* the same argument, just dressed up nicer, using functors instead of diagrams. In 1970, I was fresh from homological algebra. The construction struck me (and still does) as reminiscent of the argument you use in showing that if you have the beginnings of a map from a projective complex to an acyclic one, you can continue it one more step. The main difference was that this was a well-founded poset instead of an inter-indexed chain. And if anyone ever wondered why I called these A diagrams and P diagrams, it had nothing to do with A&P and everything to do with acyclic and projective. Thus the embedding theorem is, like many other things I have done, a form of acyclic models. From cat-dist Wed May 27 14:46:15 1998 Received: (from Majordom@localhost) by mailserv.mta.ca (8.8.8/8.8.8) id MAA27829 for categories-list; Wed, 27 May 1998 12:57:04 -0300 (ADT) X-Authentication-Warning: mailserv.mta.ca: Majordom set sender to cat-dist@mta.ca using -f Date: Wed, 27 May 1998 17:08:33 +0200 From: Matthieu Amiguet Subject: categories: Evolutive systems with memory To: categories@mta.ca Message-id: <356C2C71.22EB4BF6@etudiants.unine.ch> Organization: IIIA MIME-version: 1.0 X-Mailer: Mozilla 4.04 [en] (X11; I; SunOS 5.5.1 sun4m) Content-type: text/plain; charset=iso-8859-1 Content-transfer-encoding: 8BIT Sender: cat-dist@mta.ca Precedence: bulk Status: RO X-Status: Hello! I'm trying to get information about Ehresmann & Vanbremeersch theory of "Evolutive systems with memory". This is a theory for modelling complex evolutive systems using category theory. I've got a couple of papers (from 1989 to 1992), but I would like to find a synthtic article which could present the matter more consistently... Does anybody know if there is such a thing, or at least whom I could ask? Thank you for any help, Matthieu Amiguet Université de Neuchatel CH-2000 Neuchatel