From rrosebru@mta.ca Tue Jul 4 08:20:46 2000 -0300 Received: (from Majordom@localhost) by mailserv.mta.ca (8.9.3/8.9.3) id IAA08040 for categories-list; Tue, 4 Jul 2000 08:14:16 -0300 (ADT) X-Authentication-Warning: mailserv.mta.ca: Majordom set sender to cat-dist@mta.ca using -f Message-ID: <3961AC9E.C5F2613B@bangor.ac.uk> Date: Tue, 04 Jul 2000 10:21:34 +0100 From: Ronnie Brown X-Mailer: Mozilla 4.72 [en] (Win98; I) X-Accept-Language: en MIME-Version: 1.0 To: categories@mta.ca Subject: categories: Preprint: Globular and cubical strict multiple categories 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: 1 The following preprint is available on the xxx archive. math.CT/0007009 [abs, src, ps, other] : Title: Multiple categories: the equivalence of a globular and a cubical approach Authors: Fahd A. A. Al-Agl, Ronald Brown, Richard Steiner Comments: Latex2E, xy, 38 pages Subj-class: Category Theory; Algebraic Topology MSC-class: 18D35, 55U99 We show the equivalence of two kinds of strict multiple category, namely the well known globular omega-categories, and the cubical omega-categories with connections. (30kb) Ronnie Brown -- Prof R. Brown, School of Informatics, Mathematics Division, University of Wales, Bangor Dean St., Bangor, Gwynedd LL57 1UT, United Kingdom Tel. direct:+44 1248 382474|office: 382475 fax: +44 1248 361429 World Wide Web: home page: http://www.bangor.ac.uk/~mas010/ (Links to survey articles: Higher dimensional group theory Groupoids and crossed objects in algebraic topology) Symbolic Sculpture and Mathematics: http://www.bangor.ac.uk/SculMath/ Mathematics and Knots: http://www.bangor.ac.uk/ma/CPM/exhibit/welcome.htm From rrosebru@mta.ca Wed Jul 5 09:14:13 2000 -0300 Received: (from Majordom@localhost) by mailserv.mta.ca (8.9.3/8.9.3) id JAA26288 for categories-list; Wed, 5 Jul 2000 09:09:11 -0300 (ADT) X-Authentication-Warning: mailserv.mta.ca: Majordom set sender to cat-dist@mta.ca using -f Date: Tue, 4 Jul 2000 06:30:53 -0700 (PDT) Message-Id: <200007041330.GAA13908@Steam.Stanford.EDU> From: Fmoods Mailbox To: categories@mta.ca Subject: categories: FMOODS 2000 Call for Participation, Demos, and Posters Sender: cat-dist@mta.ca Precedence: bulk Status: O X-Status: X-Keywords: X-UID: 2 [the usual apologies for duplicates] Note that the FMOODS registration page is now available and can be accessed through the conference web site. Hotel rooms are often hard to find in Palo Alto, so booking early is advised. ============================================================================== Call for Participation Demos and Posters FMOODS 2000 IFIP TC6/WG6.1 Fourth International Conference on Formal Methods for Open Object-Based Distributed Systems Stanford University , Stanford, California, USA September 6-8, 2000 ------------------------------------------------------------------------ Electronic Information * The conference home page is found at http://www.ics.uci.edu/~fmoods2000 * Conference-related email should be addressed to fmoods2000@cs.stanford.edu * Information on the FMOODS series of conferences can be found at http://www.cs.ukc.ac.uk/research/netdist/fmoods ------------------------------------------------------------------------ Call for Posters The poster session will provide an opportunity for attendees to learn about innovative work in progress and to preview late-breaking research results. Submission instructions: Researchers interested in presenting a poster should prepare an overview of their proposed poster in the form of text or postscript file of no more than 1000 words in length. Send the poster title, and the names and affiliations of its authors (including email address), along with the overview (as text in the body of the email, or as an attachment), to: fmoods2000@steam.stanford.edu. Research students working on FMOODS relevant topics are encouraged to participate in the poster session. Deadlines: Poster abstract submission: August 15, 2000 Poster acceptance nofication: within 7-10 days after submission is received. ------------------------------------------------------------------------ Call for Demos FMOODS 2000 will include a session of software demonstrations. Submission instructions are identical to the poster submission mechanism above. All equipment should be provided by you (bring a laptop); we will provide an internet connection as well as a large display for PC-compatible computers. Demonstrations related to papers appearing at the conference are particuarly encouraged. ------------------------------------------------------------------------ Student Grants We have applied for funding to provide some student grants for attending FMOODS. If you are a student and are in need of a grant to support travel expenses send an inquiry to fmoods2000@cs.stanford.edu including your name, institution, status, and research interests (one or two lines). Priority will be given to students presenting posters. ------------------------------------------------------------------------ Invited Speakers * Jose Meseguer, SRI International * Roberto Gorrieri, U. Bologna, Italy * Jaydev Misra, U. Texas, Austin * Alan Karp, Open Systems Operation, Hewlett-Packard A preliminary program and abstracts is available from the conference web page. ------------------------------------------------------------------------ Co-located with SPIN'2000, 7th International SPIN Workshop on Model Checking of Software, to be held at Stanford the previous week August 30-31, September 1. See: http://ase.arc.nasa.gov/spin2000 ------------------------------------------------------------------------ Objectives Object-based Distributed Computing is being established as the most pertinent basis for the support of large, heterogeneous computing and telecommunications systems. Indeed, several important international organisations, such as ITU, ISO, OMG, TINA-C, etc. are defining similar distributed object-based frameworks as a foundation for open distributed computing. The advent of Open Object-based Distributed Systems - OODS - brings new challenges and opportunities for the use and development of formal methods. New architectures and system models are emerging (e.g., the enterprise, information, computational and engineering viewpoints of the ITU-T/ISO/IEC ODP Reference Model) which require formal notational support. Usual design issues such as specification, verification, refinement, and testing need to take into account new dimensions introduced by distribution and openness, such as quality of service and dependability constraints, dynamic binding and reconfiguration, consistency between multiple models and viewpoints, etc. OODS is a challenging research context and a source of motivation for semantical models of object-based systems and notations, for the evolution of standardised formal description techniques, for the application and assessment of logic based approaches, for better understanding and information modeling of business requirements, and for the further development and use of Object Oriented methodologies and tools. The objective of FMOODS is to provide an integrated forum for the presentation of research in several related fields, and the exchange of ideas and experiences in the topics concerned with the formal methods support for Open Object-based Distributed Systems. Topics of interest include but are not limited to: * formal models for object-based distributed computing * semantics of object-based distributed systems and programming languages * formal techniques in object-based and object-oriented specification, analysis and design * refinement and transformation of specifications * types, service types and subtyping * interoperability and composability of distributed services * object-based coordination languages * object-based mobile languages * efficient analysis techniques of specifications * multiple viewpoint modelling and consistency between different models * formal techniques in distributed systems verification and testing * specification, verification and testing of quality of service constraints * formal methods and object life cycle * beyond IDL: semantics based specification patterns * formal models for measuring the quality of object-oriented requirement or design specifications * formal aspects of distributed real-time multimedia systems * applications to telecommunications and related areas ------------------------------------------------------------------------ Conference Organizers Carolyn Talcott(Chair) Scott Smith(PC Chair) Tel: + 650 723-0936 Tel: + 410 516-5299 Fax: + 650 725-7411 Fax: + 410 516-6134 Stanford University The Johns Hopkins University Stanford, CA, USA Balimore, MD, USA clt@cs.stanford.edu scott@cs.jhu.edu Nalini Venkatasubramanian Sriram Sankar Tel: + 949 824-5898 Tel: + 510 796-0915 Fax: + 949 824-4056 Fax:+ 510 796-0916 University of California at Irvine Metamata Inc. Irvine, CA, USA Fremont, CA, USA nalini@ics.uci.edu sriram.sankar@metamata.com Program Committee * Gul Agha (U. of Illinois, USA) * Patrick Bellot (ENST, Paris, France) * Lynne Blair (U. Lancaster, UK) * Howard Bowman (UKC, Kent, UK) * Paolo Ciancarini (U. Bologna, Italy) * John Derrick (UKC, Kent, UK) * Michel Diaz (LAAS-CNRS, Toulouse, France) * Alessandro Fantechi (U. Firenze, Italy) * Kathleen Fisher (ATT Research Labs, USA) * Kokichi Futatsugi (Jaist, Ishikawa, Japan) * Joseph Goguen (UC San Diego, USA) * Roberto Gorrieri (U. Bologna, Italy) * Guy Leduc (U. of Liege, Belgium) * Luigi Logrippo (U of Ottawa, Canada) * David Luckham (Stanford University, USA) * Jan de Meer (GMD Fokus, Berlin, Germany) * Elie Najm (ENST, Paris, France) * Dusko Pavlovic (Kestrel Institute, USA) * Omar Rafiq (U. of Pau, France) * Arend Rensink (U. Twente, Netherlands) * Sriram Sankar (Metamata Inc., USA) * Gerd Schuermann (GMD Fokus, Berlin, Germany) * Scott Smith (Johns Hopkins University, USA) * Jean-Bernard Stefani (FT/CNET, Issy-les-Moulineaux, France) * Carolyn Talcott (Stanford University, USA) * Nalini Venkatasubramanian (UC Irvine, USA) Sponsors - IFIP ------------------------------------------------------------------------ From rrosebru@mta.ca Thu Jul 6 09:01:01 2000 -0300 Received: (from Majordom@localhost) by mailserv.mta.ca (8.9.3/8.9.3) id IAA23315 for categories-list; Thu, 6 Jul 2000 08:54:16 -0300 (ADT) X-Authentication-Warning: mailserv.mta.ca: Majordom set sender to cat-dist@mta.ca using -f Message-Id: <200007060838.AA05872@menthe.ens.fr> Content-Type: text/plain Mime-Version: 1.0 (NeXT Mail 4.2mach_patches v148.2) From: Giuseppe Longo Date: Thu, 6 Jul 2000 10:38:33 +0200 To: categories@mta.ca Subject: categories: New programs ... conference, Paris Sender: cat-dist@mta.ca Precedence: bulk Status: O X-Status: X-Keywords: X-UID: 3 Preliminary announcement: "New programs and open problems in the foundation of mathematics and of its applications, in year 2000" November 13 and 14, 2000 Ecole Normale Superieure, 45, rue d'Ulm, 75005 Paris Salle Dussane Program: A. Connes "Non-commutative Geometry" Respondent: TBA J.-Y. Girard "Locus solum" Respondent: P.-L. Curien W. Lawvere "Dialectical foundations of, by, and for mathematics" Respondent: I. Moerdijk A. Macintyre "Prospects in logic" Respondent: M. F. Coste-Roy R. Milner "The flux of computation" Respondent: G. Berry Panel discussion : "Geometric Structures in Logic, Physics and Computing" with the invitees and the members of the working group "Geometrie et Cognition" (G. Longo, chair) The Conference is open to public and it is part of the "Atelier de Recherche" Geometrie et Cognition, partly supported by the MENRT (http://www.dmi.ens.fr/users/longo/geocogni.html). Contact: longo@dmi.ens.fr http://www.dmi.ens.fr/users/longo From rrosebru@mta.ca Sat Jul 8 10:51:34 2000 -0300 Received: (from Majordom@localhost) by mailserv.mta.ca (8.9.3/8.9.3) id KAA24647 for categories-list; Sat, 8 Jul 2000 10:45:36 -0300 (ADT) X-Authentication-Warning: mailserv.mta.ca: Majordom set sender to cat-dist@mta.ca using -f Message-ID: <01BFE837.793190C0.noson@sci.brooklyn.cuny.edu> From: Noson Yanofsky Reply-To: "noson@sci.brooklyn.cuny.edu" To: "'categories@mta.ca'" Subject: categories: Preprint: Coherence, Homotopy and 2-Theories Date: Fri, 7 Jul 2000 17:19:13 -0400 Organization: Brooklyn College X-Mailer: Microsoft Internet E-mail/MAPI - 8.0.0.4211 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: 4 The following preprint is available on the xxx.lanl.gov archive: http://xxx.lanl.gov/abs/math.CT/0007033 Coherence, Homotopy and 2-Theories Authors: Noson S. Yanofsky Comments: 32 pages; XY-Pic Subj-class: Category Theory; Quantum Algebra MSC-class: 18D10; 18C10; 55U35 2-Theories are a canonical way of describing categories with extra structure. 2-theory-morphisms are used when discussing how one structure can be replaced with another structure. This is central to categorical coherence theory. We place a Quillen model category structure on the category of 2-theories and 2-theory-morphisms where the weak equivalences are biequivalences of 2-theories. A biequivalence of 2-theories (Morita equivalence) induces and is induced by a biequivalence of 2-categories of algebras. This model category structure allows one to talk of the homotopy of 2-theories and discuss the universal properties of coherence. All the best, Noson From rrosebru@mta.ca Sat Jul 8 19:57:18 2000 -0300 Received: (from Majordom@localhost) by mailserv.mta.ca (8.9.3/8.9.3) id TAA29242 for categories-list; Sat, 8 Jul 2000 19:56:14 -0300 (ADT) X-Authentication-Warning: mailserv.mta.ca: Majordom set sender to cat-dist@mta.ca using -f Message-ID: <000a01bfe8fe$f2328e80$847979a5@osherphd> From: "Osher Doctorow" To: Subject: categories: Cross-category "conversions" of some interest Date: Sat, 8 Jul 2000 10:05:44 -0700 MIME-Version: 1.0 Content-Type: multipart/alternative; boundary="----=_NextPart_000_0007_01BFE8C4.150BEB80" 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 Sender: cat-dist@mta.ca Precedence: bulk Status: RO X-Status: X-Keywords: X-UID: 5 This is a multi-part message in MIME format. ------=_NextPart_000_0007_01BFE8C4.150BEB80 Content-Type: text/plain; charset="iso-8859-1" Content-Transfer-Encoding: quoted-printable From: Osher Doctorow, Ph.D. osher@ix.netcom.com, Sat. July 7, 2000, = 9:46AM Dear Colleagues: I have been studying the "conversion" from x/y to 1 - x + y and the = conversion from x/y to x + y - xy, where x and y are elements of any = category (although in practice I have been restricting attention to = probability-statistics (x =3D Pr(A), y =3D Pr(AB) where AB is the = intersection of sets/events A and B) and (fuzzy) multivalued logics such = as Goguen/Product (G) and Lukaciewicz (L) and Godel (Go) (in the case = of G, x/y is the non-trivial implication x --> y and in the case of L, 1 = - x + y is the non-trivial implication x --> y) and the Jacobson radical = in ring theory (which is based on the circle composition product x*y =3D = x + y - xy for x and y elements of the ring) and Fermat's Last Theorem = in number theory (x and y are integers and a super-super short proof = seems to depend on generalizing x*y to n dimensions and using the = conjugate which will be described below). The conjugate ^ of 1 - x + y = is (1 - x + y)^ =3D 1 + x - y, and the conjugate of x + y - xy is x + y = + xy. An n dimensional generalization would involve x^^n + y^^n = where ^^ is exponentiation (unrelated to ^) since the product of 1 - x + = y and its conjugate can be shown to involve x^^2 + y^^2 - x^^2 y^^2 =3D = x^^2 * y^^2 and so on. The expression "conversion" is used above = instead of function because y/x --> 1 - x + y is not a function but a = conversion of the division operation (for x non-zero) to subtraction and = the addition of 1. =20 The probability-statistics reader may recognize x/y and (Bayesian) = conditional probability (BCP for short) written Pr(B/A) for Pr(A) = non-zero, and it turns out that 1 - x + y for probability-statistics is = Pr(A-->B) =3D Pr(A' U B) =3D Pr(A' ) + Pr(B) - Pr(A' B) =3D Pr(A' ) + = Pr(AB) =3D 1 - Pr(A) + P(AB), which latter expression is maximized for = very rare events and lower dimensional events when probability = distributions are continuous on a volume of space containing A and B = (Pr(A) =3D 0 for those cases) and also when A is a subset of B. = Pr(A-->B) is abbreviated LBP for logic-based probability, which I have = been developing since 1980. BCP applies to frequent/common and = independent-like or low influence events (including Markov processes = which have many similarities to independent events although they are = "slightly" dependent) and LBP applies to rare events or rare-like events = (Pr(A) less than epsilon for epsilon small positive) and to n-k = dimensional subset events of n-dimensional Euclidean space for k =3D 0 = to n and to highly dependent or highly one or two-way influencing = events.=20 As for Goguen/Product logic (G) and Lukaciewicz logic, their union or = "join" G U L, similarly to the union or join of either of them with = Godel logic G, equals BL2, the basic (fuzzy) multi-valued logic which = generalizes Boolean logic with the deduction Theorem and the plausible = axiom p V ~p (p or ~p) for each proposition p. Thus, G and L = constitute all of the universe of logic in this sense, and they = partition it into disjoint "roughly equal" parts. Osher Doctorow Doctorow Consultants Culver City, California USA =20 =20 ------=_NextPart_000_0007_01BFE8C4.150BEB80 Content-Type: text/html; charset="iso-8859-1" Content-Transfer-Encoding: quoted-printable
From: Osher Doctorow, Ph.D. osher@ix.netcom.com, Sat. July = 7, 2000,=20 9:46AM
 
Dear Colleagues:
 
I have been studying = the "conversion" from x/y=20 to 1 - x + y and the conversion from x/y to x + y - xy, where x and y = are=20 elements of any category (although in practice I have been restricting = attention=20 to probability-statistics (x =3D Pr(A), y =3D Pr(AB) where AB is = the=20 intersection of sets/events A and B) and (fuzzy) multivalued logics = such as=20 Goguen/Product (G) and Lukaciewicz (L) and Godel (Go)  (in the case = of G,=20 x/y is the non-trivial implication x --> y and in the case of L, 1 - = x + y is=20 the non-trivial implication x --> y) and the Jacobson radical in ring = theory=20 (which is based on the circle composition product x*y =3D x + y - xy for = x and y=20 elements of the ring) and Fermat's Last Theorem in number theory (x = and y=20 are integers and a super-super short proof seems to depend on = generalizing=20 x*y to n dimensions and using the conjugate which will be described=20 below).  The conjugate ^ of 1 - x + y is (1 - x + y)^ =3D 1 + = x - y, and=20 the conjugate of x + y - xy is x + y + xy.    An n=20 dimensional generalization would involve x^^n + y^^n  where ^^ = is=20 exponentiation (unrelated to ^) since the product of 1 - x + y and its = conjugate=20 can be shown to involve x^^2 + y^^2 - x^^2 y^^2 =3D x^^2 * y^^2 and = so=20 on.  The expression "conversion" is used above instead of function=20 because y/x --> 1 - x + y is not a function but a conversion of = the=20 division operation (for x non-zero) to subtraction and the addition of = 1. =20   
 
The probability-statistics reader may = recognize x/y=20 and (Bayesian) conditional probability (BCP for short) written = Pr(B/A) for=20 Pr(A) non-zero, and it turns out that 1 - x + y for = probability-statistics=20 is Pr(A-->B) =3D Pr(A' U B) =3D Pr(A' ) + Pr(B) - Pr(A' B) =3D Pr(A' = ) + Pr(AB) =3D 1=20 - Pr(A) + P(AB), which latter expression is maximized for very rare = events=20 and lower dimensional events when probability distributions are = continuous=20 on a volume of space containing A and B (Pr(A) =3D 0 for = those cases) and=20 also when A is a subset of B.  Pr(A-->B) is abbreviated LBP for=20 logic-based probability, which I have been developing since = 1980.  =20 BCP applies to frequent/common and independent-like or low influence = events=20 (including Markov processes which have many similarities to=20 independent events although they are "slightly" dependent) and LBP = applies=20 to rare events or rare-like events (Pr(A) less than epsilon for epsilon = small=20 positive) and to n-k dimensional subset events of n-dimensional = Euclidean space=20 for k =3D 0 to n and to highly dependent or highly one or two-way = influencing=20 events. 
 
As for Goguen/Product logic = (G) and=20 Lukaciewicz logic, their union or "join" G U L, similarly to the union=20 or join of either of them with Godel logic G, equals BL2, the = basic=20 (fuzzy) multi-valued logic which generalizes Boolean logic with the = deduction=20 Theorem and the plausible axiom p V ~p (p or ~p) for each proposition=20 p.   Thus, G and L constitute all of the universe of = logic in=20 this sense, and they partition it into disjoint "roughly equal"=20 parts.
 
Osher Doctorow
Doctorow Consultants
Culver City, California = USA   =20
 
  
------=_NextPart_000_0007_01BFE8C4.150BEB80-- From rrosebru@mta.ca Tue Jul 11 11:49:32 2000 -0300 Received: (from Majordom@localhost) by mailserv.mta.ca (8.9.3/8.9.3) id LAA15592 for categories-list; Tue, 11 Jul 2000 11:48:49 -0300 (ADT) X-Authentication-Warning: mailserv.mta.ca: Majordom set sender to cat-dist@mta.ca using -f Message-Id: <4.1.20000711092633.00a0c110@mail.oberlin.net> X-Sender: cwells@mail.oberlin.net X-Mailer: QUALCOMM Windows Eudora Pro Version 4.1 Date: Tue, 11 Jul 2000 09:28:04 -0700 To: categories@mta.ca From: Charles Wells Subject: categories: Saturated functors 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 KAA22619 Sender: cat-dist@mta.ca Precedence: bulk Status: RO X-Status: X-Keywords: X-UID: 6 Can anyone tell me what Ehresmann meant by a "saturated functor" (foncteur saturé) in 1967? Charles Wells, Oberlin, Ohio, 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 Wed Jul 12 10:29:31 2000 -0300 Received: (from Majordom@localhost) by mailserv.mta.ca (8.9.3/8.9.3) id KAA13924 for categories-list; Wed, 12 Jul 2000 10:25:47 -0300 (ADT) X-Authentication-Warning: mailserv.mta.ca: Majordom set sender to cat-dist@mta.ca using -f Message-ID: <000201bfeb66$d41068e0$edf46ed1@osherphd> From: "Osher Doctorow" To: Subject: categories: Re: Cross-category "conversions" of some interest Date: Tue, 11 Jul 2000 11:27:52 -0700 MIME-Version: 1.0 Content-Type: multipart/alternative; boundary="----=_NextPart_000_0007_01BFEB2B.0D635D00" 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 Sender: cat-dist@mta.ca Precedence: bulk Status: O X-Status: X-Keywords: X-UID: 7 This is a multi-part message in MIME format. ------=_NextPart_000_0007_01BFEB2B.0D635D00 Content-Type: text/plain; charset="iso-8859-1" Content-Transfer-Encoding: quoted-printable From: Osher Doctorow osher@ix.netcom.com, Tues. July 11, 2000, 11:00AM Dear Colleagues: The "conversions" from x/y to 1 - x + y and from x/y to x + y - xy which = I introduced here on July 8, 2000 not only can be used across = probability-statistics and (fuzzy) multivalued logical categories and = ring theory and number theory categories (Fermat's Last Theorem) as = indicated in that paper, but they are especially useful in special = relativity and quantum field theory as well as quantum mechanics as I = shall show here. The categories in the latter two fields will be = discussed in detail later, but here I would like to indicate what = results are obtained. Applying the conversion from x/y to 1 - x + y to the Heisenberg = Uncertainty Principle in the form xy > k where k is a positive constant = (x, y uncertainties in position and momentum respectively, for example, = where notice x and y are nonnegative in the standard deviation version = of uncertainty) yields xy =3D (x/y)y^^2 (where ^^ is exponentiation) --> = (1 - x + y)y^^2. For 1 - x + y < 0, which says x > 1 + y, the latter = expression is negative, so the converted form reads: (1 - x + y)y^^2 =3D = -/1 - x + y/y^^2 > k and therefore /1 - x + y/y^^2 < -k for k positive. = Since y^^2 is always nonnegative, this conditional holds trivially = (always) provided that x > 1 + y. Since x and y could be selected with = exchanged physical roles (uncertainties in momentum and position = respectively, for example), the condition that x > 1 + y is rather = arbitrary and certainly will be fulfilled for one of the two orders in = which x and y are defined. The conclusion which we must come to is that there are two phases: the = phase in which the Heisenberg Uncertainty Principle is satisfied (which = phase may for example correspond to an interaction between macroscopic = observation and microscopic phenomena) and the phase in which the = Heisenberg Uncertainty Principle is not satisfied (which phrase may = correspond to two macroscopic or two microscopic observation/phenomena = pairs or both or some other regime). A similar but even more explicit results holds when we make the = conversion in special relativity in the beta or 1/beta Lorentz = contraction factor sqrt(1 - v^^2/c^^2) where sqrt means square root of. = We get 1 - v^^2/c^^2 =3D 1 - (v/c)^^2 =3D 1 - y/x for y =3D v^^2, x =3D = c^^2 and this goes over to 1 - (1 - x + y =3D x - y. So beta or 1/beta = (depending on what notation one uses) goes over to sqrt(x - y). = However, it has been pointed out in earlier papers (and it will be = pointed out again) that the closure law holds in most of the categories = to which these conversions x/y --> 1 - x + y for example apply, and let = us assume the same thing here (closure under subtraction means that if x = and y are in the category or in the set part of the category other than = the morphism, then x - y and y - x are also in the set part). = Therefore, sqrt(y - x) is an alternate form of the result for beta or = 1/beta, and since sqrt (y - x) is imaginary when y < x and real when y < = x, it must be that the real and imaginary scales are themselves = arbitrary. In more common terminology, they merely measure different = phases in the sense of liquid-solid-gas etc. Thus, not only can the speed of light be exceeded (although the object = exceeding it enters a different phase), but the Heisenberg Uncertainty = Principle can be violated (but the objects violating it enter different = phases). This is not surprising in view of the superluminal group = velocity results obtained in 1997 and later experiments by Nimtz in = Cologne/Koln and Berkeley and elsewhere (which according to Nimtz are = also applicable to ordinary velocities). It is also not surprising in = view of M. Jammer's comprehensive analysis (The Philosophy of Quantum = Mechanics, Wiley: New York 1974) of the Heisenberg Uncertainty Principle = in which it is found that the principle does not apply to individual = measurements of physical objects but to statistical summaries of their = uncertainties (Schrodinger in fact proved that on Hilbert Space = self-adjoint operators obey this inequality for the product of their = uncertainties, but Banach Space is far more general than Hilbert Space = and gives enough room by far to define or contain a second phase sets of = objects - which may not be operators in the usual sense). The implications for special relativity and for quantum field theory = (which combines quantum mechanics with special relativity) are obviously = serious, although not necessarily catastrophic. It just means that = these theories are again approximations to one or two states or category = of states of physical objects but not to more general or different = categories of states of physical objects. Since light itself satisfies = both categories (sqrt (1 -(c^^2/c^^2)) is 0 which can be regarded as = both real and imaginary), there certainly is at least one non-empty = element in each category. Osher Doctorow Doctorow Consultants Culver City, California USA =20 ------=_NextPart_000_0007_01BFEB2B.0D635D00 Content-Type: text/html; charset="iso-8859-1" Content-Transfer-Encoding: quoted-printable
From: Osher Doctorow osher@ix.netcom.com, Tues. July = 11, 2000,=20 11:00AM
 
Dear Colleagues:
 
The "conversions" from x/y to 1 - x + y = and from=20 x/y to x + y - xy which I introduced here on July 8, 2000 not only can = be used=20 across probability-statistics and (fuzzy) multivalued logical categories = and=20 ring theory and number theory categories (Fermat's Last Theorem) as = indicated in that paper, but they are especially useful in special = relativity=20 and quantum field theory as well as quantum mechanics as I shall = show=20 here.  The categories in the latter two fields will be discussed in = detail=20 later, but here I would like to indicate what results are = obtained.
 
Applying the conversion from x/y = to 1 - x + y=20 to the Heisenberg Uncertainty Principle in the form xy > k where = k is a=20 positive constant (x, y uncertainties in position and momentum=20 respectively, for example, where notice x and y are nonnegative in the = standard=20 deviation version of uncertainty) yields xy =3D (x/y)y^^2 (where ^^ is=20 exponentiation) --> (1 - x + y)y^^2.  For 1 - x + y = < 0,=20 which says x > 1 + y, the latter expression is negative, so the=20 converted form reads: (1 - x + y)y^^2 =3D -/1 - x + y/y^^2 > k = and=20 therefore /1 - x + y/y^^2 < -k for k positive.  Since y^^2 is = always=20 nonnegative, this conditional holds trivially (always) provided = that x >=20 1 + y.   Since x and y could be selected with = exchanged=20 physical roles (uncertainties in momentum and position respectively, for = example), the condition that x > 1 + y is rather arbitrary and = certainly will=20 be fulfilled for one of the two orders in which x and y are=20 defined.
 
The conclusion which we must come to is = that there=20 are two phases: the phase in which the Heisenberg Uncertainty Principle = is=20 satisfied (which phase may for example correspond to an interaction = between=20 macroscopic observation and microscopic phenomena) and the phase in = which the=20 Heisenberg Uncertainty Principle is not satisfied (which phrase may = correspond=20 to two macroscopic or two microscopic observation/phenomena pairs or = both or=20 some other regime).
 
A similar but even more explicit = results holds when=20 we make the conversion in special relativity in the beta or 1/beta = Lorentz=20 contraction factor sqrt(1 - v^^2/c^^2) where sqrt means square root = of.  We=20 get 1 - v^^2/c^^2 =3D 1 - (v/c)^^2 =3D 1 - y/x for y =3D v^^2, = x =3D c^^2 and=20 this goes over to 1 - (1 - x + y =3D x - y.   So = beta or=20 1/beta (depending on what notation one uses) goes over to sqrt(x - = y). =20 However, it has been pointed out in earlier papers (and it = will be=20 pointed out again) that the closure law holds in most of the = categories to=20 which these conversions x/y --> 1 - x + y for example apply, and let = us=20 assume the same thing here (closure under subtraction means that if x = and y are=20 in the category or in the set part of the category other than the = morphism, then=20 x - y and y - x are also in the set part).   Therefore, sqrt(y = - x) is=20 an alternate form of the result for beta or 1/beta, and since sqrt (y - = x) is=20 imaginary when y < x and real when y < x, it must be that the = real=20 and imaginary scales are themselves arbitrary.  In more common = terminology,=20 they merely measure different phases in the sense = of liquid-solid-gas=20 etc.
 
Thus, not only can the speed of = light be=20 exceeded (although the object exceeding it enters a different phase), = but the=20 Heisenberg Uncertainty Principle can be violated (but the objects = violating it=20 enter different phases).    This is not surprising = in view=20 of the superluminal group velocity results obtained in 1997 and later=20 experiments by Nimtz in Cologne/Koln and Berkeley and elsewhere (which = according=20 to Nimtz are also applicable to ordinary velocities).  It is also = not=20 surprising in view of M. Jammer's comprehensive analysis (The Philosophy = of=20 Quantum Mechanics, Wiley: New York 1974) of the Heisenberg = Uncertainty=20 Principle in which it is found that the principle does not apply to = individual=20 measurements of physical objects but to statistical summaries of their=20 uncertainties (Schrodinger in fact proved that on Hilbert Space = self-adjoint=20 operators obey this inequality for the product of their uncertainties, = but=20 Banach Space is far more general than Hilbert Space and gives enough = room by far=20 to define or contain a second phase sets of objects - which may not be = operators=20 in the usual sense).
 
The implications for special relativity = and for=20 quantum field theory (which combines quantum mechanics with special = relativity)=20 are obviously serious, although not necessarily = catastrophic.   It=20 just means that these theories are again approximations to one or two = states or=20 category of states of physical objects but not to more general or = different=20 categories of states of physical objects.  Since light=20 itself satisfies both categories (sqrt (1 -(c^^2/c^^2)) is 0 which = can be=20 regarded as both real and imaginary), there certainly is at least one = non-empty=20 element in each category.
 
Osher Doctorow
Doctorow Consultants
Culver City, California=20 USA   
------=_NextPart_000_0007_01BFEB2B.0D635D00-- From rrosebru@mta.ca Wed Jul 12 10:29:35 2000 -0300 Received: (from Majordom@localhost) by mailserv.mta.ca (8.9.3/8.9.3) id KAA09488 for categories-list; Wed, 12 Jul 2000 10:26:48 -0300 (ADT) X-Authentication-Warning: mailserv.mta.ca: Majordom set sender to cat-dist@mta.ca using -f Message-ID: <000001bfeb8e$fa331b80$74f46ed1@osherphd> From: "Osher Doctorow" To: Subject: categories: category theory analysis of the Jacobson radical Date: Tue, 11 Jul 2000 16:20:52 -0700 MIME-Version: 1.0 Content-Type: multipart/alternative; boundary="----=_NextPart_000_000F_01BFEB53.FB901540" 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 Sender: cat-dist@mta.ca Precedence: bulk Status: O X-Status: X-Keywords: X-UID: 8 This is a multi-part message in MIME format. ------=_NextPart_000_000F_01BFEB53.FB901540 Content-Type: text/plain; charset="iso-8859-1" Content-Transfer-Encoding: quoted-printable From: Osher Doctorow osher@ix.netcom.com, Tues. July 11, 2000, 4:15PM Dear Colleagues: The Jacobson radical that I have been mentioning in the last several = communications, and which is defined in terms of the circle composition = product x * y =3D x + y - xy, is related to category theory by M. W. = Gray (Pacific Jour. Math 1967, vol. 23, 79-89 and her book A radical = approach to algebra, Addison-Wesley: Reading, 1970. In particular, the = semiabelian category was introduced by her to include various of the = radicals including the Jacobson radical. A very accessible detailed = presentation of her work and those of others up to 1994 is T. W. Palmer = Banach algebras and the general theory of *-algebras volume I: algebras = and Banach algebras, Cambridge University Press: Cambridge, which is = part of the exceptionally valuable Encyclopedia of Mathematics and Its = Applications of the Cambridge University Press (not of course a usual = encyclopedia - the name is used for numerous separate books of the = highest quality on crucial mathematical subjects important in the latest = rsearch). See especially sections 4.3 and 4.7. I will give more details on this at a future time. Osher Doctorow ------=_NextPart_000_000F_01BFEB53.FB901540 Content-Type: text/html; charset="iso-8859-1" Content-Transfer-Encoding: quoted-printable
From: Osher Doctorow osher@ix.netcom.com, Tues. July = 11, 2000,=20 4:15PM
 
Dear Colleagues:
 
The Jacobson radical that I have been = mentioning in=20 the last several communications, and which is defined in terms of the = circle=20 composition product x * y =3D x + y - xy, is related to category theory = by M. W.=20 Gray (Pacific Jour. Math 1967, vol. 23, 79-89 and her book A radical = approach to=20 algebra, Addison-Wesley: Reading, 1970.  In particular, the = semiabelian=20 category was introduced by her to include various of the radicals = including the=20 Jacobson radical.  A very accessible detailed presentation of her = work and=20 those of others up to 1994 is T. W. Palmer Banach algebras and the = general=20 theory of *-algebras volume I: algebras and Banach algebras, Cambridge=20 University Press: Cambridge, which is part of the exceptionally valuable = Encyclopedia of Mathematics and Its Applications of the Cambridge = University=20 Press (not of course a usual encyclopedia - the name is used for = numerous=20 separate books of the highest quality on crucial mathematical subjects = important=20 in the latest rsearch).   See especially sections 4.3 and=20 4.7.
 
I will give more details on this at a = future=20 time.
 
Osher Doctorow
 
------=_NextPart_000_000F_01BFEB53.FB901540-- From rrosebru@mta.ca Thu Jul 13 09:54:17 2000 -0300 Received: (from Majordom@localhost) by mailserv.mta.ca (8.9.3/8.9.3) id JAA07546 for categories-list; Thu, 13 Jul 2000 09:49:14 -0300 (ADT) X-Authentication-Warning: mailserv.mta.ca: Majordom set sender to cat-dist@mta.ca using -f From: "Julio Pereira Machado" Reply-to: juliopm@portoweb.com.br To: categories@mta.ca Date: Wed, 12 Jul 2000 11:22:02 -300 Subject: categories: request info on Topos X-Mailer: DMailWeb Web to Mail Gateway 2.2s, http://netwinsite.com/top_mail.htm Message-id: <396c7f0a.16f.0@portoweb.com.br> X-User-Info: 143.54.7.154 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 LAA12939 Sender: cat-dist@mta.ca Precedence: bulk Status: O X-Status: X-Keywords: X-UID: 9 Hello, I´m beginning a MSc course on Computer Science. I started working with categories (specially topos)and coherence spaces and I´m looking for some papers and basic references on this subject. I´d be glad if you could help me. The main goal of my work is to define the categories (or subcategories) of STAB (coherence spaces and stable functions) and LIN (coherence spaces and linear functions) as Topos. Any suggestions are welcome. Thanks in advance, Simone Costa. From rrosebru@mta.ca Thu Jul 13 10:03:35 2000 -0300 Received: (from Majordom@localhost) by mailserv.mta.ca (8.9.3/8.9.3) id JAA11334 for categories-list; Thu, 13 Jul 2000 09:49:53 -0300 (ADT) X-Authentication-Warning: mailserv.mta.ca: Majordom set sender to cat-dist@mta.ca using -f From: claus@orchid.inf.tu-dresden.de (Claus Juergensen) Date: Wed, 12 Jul 2000 16:53:05 +0200 (MET DST) Message-Id: <200007121453.QAA01979@swt1011.inf.tu-dresden.de> To: categories@mta.ca Subject: categories: concrete functors between categories of algebras X-Sun-Charset: US-ASCII Sender: cat-dist@mta.ca Precedence: bulk Status: O X-Status: X-Keywords: X-UID: 10 Let C be a category and F, G : C -> C be endo-functors. I denote the category of all F-algebras by Alg_C F and the canonical forgettable functor by U_F : Alg_C F -> C. I'm interested in concrete functors H : Alg_C F -> Alg_C G where `concrete' indicates the property U_F = U_G . H Does anybody know about such functors? Thanks for any help/references! Claus -------------------------------------------------------------------------------- Dipl.-Math. Claus Juergensen | Technische Universitaet Dresden e-mail: claus@orchid.inf.tu-dresden.de | Fakultaet Informatik phone: +49 (0)3 51 46 3 - 82 53 | Institut fuer Theoretische Informatik Lehrstuhl Grundlagen der Programmierung | D-01062 Dresden http://orchid.inf.tu-dresden.de/gdp/ | Germany -------------------------------------------------------------------------------- From rrosebru@mta.ca Thu Jul 13 10:09:20 2000 -0300 Received: (from Majordom@localhost) by mailserv.mta.ca (8.9.3/8.9.3) id JAA19057 for categories-list; Thu, 13 Jul 2000 09:50:57 -0300 (ADT) X-Authentication-Warning: mailserv.mta.ca: Majordom set sender to cat-dist@mta.ca using -f From: S.J.Vickers@open.ac.uk Message-ID: To: categories@mta.ca Subject: categories: Re: Cross-category "conversions" of some interest Date: Wed, 12 Jul 2000 16:47:21 +0100 MIME-Version: 1.0 X-Mailer: Internet Mail Service (5.5.2650.21) Content-Type: text/plain; charset="iso-8859-1" Sender: cat-dist@mta.ca Precedence: bulk Status: O X-Status: X-Keywords: X-UID: 11 Applying the conversion from x/y to 1 - x + y to the Heisenberg Uncertainty Principle in the form xy > k where k is a positive constant (x, y uncertainties in position and momentum respectively, for example, where notice x and y are nonnegative in the standard deviation version of uncertainty) yields xy = (x/y)y^^2 (where ^^ is exponentiation) --> (1 - x + y)y^^2. For 1 - x + y < 0, which says x > 1 + y, the latter expression is negative, so the converted form reads: (1 - x + y)y^^2 = -/1 - x + y/y^^2 > k and therefore /1 - x + y/y^^2 < -k for k positive. Since y^^2 is always nonnegative, this conditional holds trivially (always) provided that x > 1 + y. Since x and y could be selected with exchanged physical roles (uncertainties in momentum and position respectively, for example), the condition that x > 1 + y is rather arbitrary and certainly will be fulfilled for one of the two orders in which x and y are defined. : Osher Doctorow Doctorow Consultants Culver City, California USA Even more strikingly, consider the identity 0/1 = 0 of classical mathematics. Applying the conversion we find 0/1 --> 1 - 0 + 1 = 2 and deduce 2 = 0, thus giving an unbelievably simple explanation of the Pauli exclusion principle for fermions. Steve Vickers. From rrosebru@mta.ca Thu Jul 13 10:18:26 2000 -0300 Received: (from Majordom@localhost) by mailserv.mta.ca (8.9.3/8.9.3) id JAA10126 for categories-list; Thu, 13 Jul 2000 09:52:02 -0300 (ADT) X-Authentication-Warning: mailserv.mta.ca: Majordom set sender to cat-dist@mta.ca using -f Message-Id: <3.0.3.32.20000712184546.006983ac@mailx.u-picardie.fr> X-Sender: ehres@mailx.u-picardie.fr X-Mailer: QUALCOMM Windows Eudora Light Version 3.0.3 (32) Date: Wed, 12 Jul 2000 18:45:46 +0200 To: categories@mta.ca From: Andree Ehresmann Subject: categories: Answer to Charles Wells 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 NAA13402 Sender: cat-dist@mta.ca Precedence: bulk Status: O X-Status: X-Keywords: X-UID: 12 In answer to Charles Wells >Can anyone tell me what Ehresmann meant by a "saturated functor" >(foncteur saturé) in 1967? Charles Ehresmann defined a "homomorphism saturated functor" already in his lectures in 1962, and it figures in his 1963 paper "Categories structurees" (Annales ENS), reprinted in "Charles Ehresmann: Oeuvres completes et Commentees", Part III-1, Amiens 1980, p. 29 In the "Comments" in this book I have given English translations in more modern terms of the main categorical definitions and results of Charles, which, up to the seventies, were often written in a non-usual style, very difficult to decipher to-day (and even at that moment for most readers, which explains they were not as widely known as they should have been!) In particular in the Note 29-2 (p. 348-9 of this book) I have translated the definition in more modern terms: A "homomorphism saturated functor" p: H -> C is a faithful amnestic functor which creates isomorphisms; amnestic means that an isomorphism mapped on an identity is an identity. Thus H is a concrete category over C, such that the restriction of p to the groupoid of isomorphisms of H is a discrete op-fibration. (there are more information in this Note). From rrosebru@mta.ca Fri Jul 14 06:24:12 2000 -0300 Received: (from Majordom@localhost) by mailserv.mta.ca (8.9.3/8.9.3) id GAA06415 for categories-list; Fri, 14 Jul 2000 06:20:44 -0300 (ADT) X-Authentication-Warning: mailserv.mta.ca: Majordom set sender to cat-dist@mta.ca using -f Date: Thu, 13 Jul 2000 16:33:03 -0400 (EDT) From: Peter Freyd Message-Id: <200007132033.e6DKX3K00348@saul.cis.upenn.edu> To: categories@mta.ca Subject: categories: film functor Sender: cat-dist@mta.ca Precedence: bulk Status: O X-Status: X-Keywords: X-UID: 13 The Dutch film "Antonia" written and directed by Marleen Gorris won the 1996 Oscar for best foreign language film. There's a scene in which the 20-year-old granddaughter of the title character is at a blackboard with a lot of exact sequences. She says (quoting the English subtitles): We will assume that the singular chain complex of the empty set equals zero. With theorem 5.8 this implies that the nth homology group is the same as the nth relative homology group if we take the subspace as the empty set. New we can construct a functor from the category....from the category Top to the category of chain complexes. Define the functor S* as follows: S* sends the ordered pair to the singular chain complex of the space X divided by the complex of A. Is this the first commercial film with categories and functors? (It's not the first with homological algebra: in 1980 "It's My Turn" opened with its lead at a blackboard proving the snake lemma.) It should be noted that the categories and functors in "Antonia" turn out to be foreplay: the speaker makes eye contact with a guy in her audience and the next scene instantly transports them from the classroom to the bedroom. From rrosebru@mta.ca Fri Jul 14 10:06:04 2000 -0300 Received: (from Majordom@localhost) by mailserv.mta.ca (8.9.3/8.9.3) id KAA22925 for categories-list; Fri, 14 Jul 2000 10:04:37 -0300 (ADT) X-Authentication-Warning: mailserv.mta.ca: Majordom set sender to cat-dist@mta.ca using -f Date: Fri, 14 Jul 2000 09:01:27 -0400 (EDT) From: Peter Freyd Message-Id: <200007141301.e6ED1RC00077@saul.cis.upenn.edu> To: categories@mta.ca Subject: categories: We're more useful than Millennium Domes Sender: cat-dist@mta.ca Precedence: bulk Status: O X-Status: X-Keywords: X-UID: 14 Copyright 2000 Times Newspapers Limited The Times (London) July 14, 2000, Friday SECTION: Home news LENGTH: 189 words HEADLINE: Dome useless, says Duke BYLINE: Dominic Kennedy BODY: A smiling Duke of Edinburgh yesterday sabotaged the Pounds 2 million campaign to save the Millennium Dome by suggesting the attraction was a useless waste of money. As the Dome opened an advertising campaign with the slogan "You've got a mind of your own, take it to the Dome", the Duke decided it was an apt time to deliver his own verdict. As he opened a new Pounds 56 million Centre for Mathematical Studies at Cambridge University, of which he is Chancellor, he did a quick calculation. "This is", he said as he unveiled a commemorative plaque, "a lot less expensive than the Dome." The audience laughed so heartily that, warming to his theme, the Duke added: "And I think it's going to be a great deal more useful." From rrosebru@mta.ca Sun Jul 16 12:11:44 2000 -0300 Received: (from Majordom@localhost) by mailserv.mta.ca (8.9.3/8.9.3) id MAA12311 for categories-list; Sun, 16 Jul 2000 12:02:57 -0300 (ADT) X-Authentication-Warning: mailserv.mta.ca: Majordom set sender to cat-dist@mta.ca using -f Message-ID: <000e01bfedad$0bf82480$aa7079a5@osherphd> From: "Osher Doctorow" To: Subject: categories: Re: Cross-Category "conversions" of some interest Date: Fri, 14 Jul 2000 09:02:39 -0700 MIME-Version: 1.0 Content-Type: multipart/alternative; boundary="----=_NextPart_000_000B_01BFED72.43157E80" 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 Sender: cat-dist@mta.ca Precedence: bulk Status: O X-Status: X-Keywords: X-UID: 15 This is a multi-part message in MIME format. ------=_NextPart_000_000B_01BFED72.43157E80 Content-Type: text/plain; charset="iso-8859-1" Content-Transfer-Encoding: quoted-printable From: Osher Doctorow osher@ix.netcom.com, Friday July 14, 2000, 8:47AM Dear Colleagues: Dr. S. J. Vickers has found two typographical errors in my July 12 = contribution which might well lead someone to conclude that an erroneous = one-sided operation on an inequality had been made. The statement = "....so the converted form reads: (1 - x + y)y^^2 =3D -/1 - x + y/y^^2 > = k," shoud have a second constant k1 or k2 (it is arbitrary which = notation is used) replacing k. I used the same k by a typographical = error and also because I had skipped an intermediate step and in my = haste used the same constant k from before. The intermediate step was = merely to consider what happens to xy when the conversion of y/x to 1 - = x + y is made. Then xy converts to (1 - x + y)y^^2 =3D -/1 - x + = y/y^^2 in the case when 1 - x + y < 0, and this is obviously = nonpositive, so -/1 - x + y/y^^2 < k2 with k2 =3D 0 for example. For 1 = - x + y > 0, we have xy converting to /1 - x + y/y^^2 which is = nonnegative and therefore /1 - x + y/y^^2 > =3D k2 with k2 =3D 0 again. = Vickers' criticism turned out to be very fortunate, not only for = clarifying the typographical error and avoiding the wrong conclusion = that I operated on only one side of an inequality when converting xy to = the other form, but also in my developing a detailed argument concerning = when the conversion from y/x to 1 - x + y becomes an actual function. = This occurs, for example, when y/x is a reduced proper or improper = fraction in the sense that numerator and denominator have no common = primes, in which case the unique factorization into primes and = consideration of the three cases y/x > 1 and y/x < 1 and y/x =3D 1 leads = to the conclusion that the conversion is a function. Thus, on the = reduced rationals, we have a function. This is not a bad set to work = with mathematically, and certainly provides a nontrivial case where the = conversion is a function and is accurate. I hope that S. J. Vickers will continue to contribute to further = discussion in this thread because of his important contributions, = provided of course that he continues to emphasize the correction of = errors and ways of further applying the conversions. If somebody finds = any further errors in my future writings, please give me the benefit of = considering the possibility that I made a typographical error. Osher Doctorow =20 ------=_NextPart_000_000B_01BFED72.43157E80 Content-Type: text/html; charset="iso-8859-1" Content-Transfer-Encoding: quoted-printable
From: Osher Doctorow osher@ix.netcom.com, Friday July = 14, 2000,=20 8:47AM
 
Dear Colleagues:
 
Dr. S. J. Vickers has found two = typographical=20 errors in my July 12 contribution which might well lead someone to = conclude that=20 an erroneous one-sided operation on an inequality had been made.  = The=20 statement "....so the converted form reads: (1 - x + y)y^^2 =3D -/1 - x = + y/y^^2=20 > k," shoud have a second constant k1 or k2 (it is arbitrary which = notation=20 is used) replacing k.  I used the same k by a typographical error = and also=20 because I had skipped an intermediate step and in my haste used the same = constant k from before.  The intermediate step was merely to = consider what=20 happens to xy when the conversion of y/x to 1 - x + y is = made.   Then=20 xy converts to (1 - x + y)y^^2 =3D -/1 - x + y/y^^2 in the case = when 1 - x +=20 y < 0, and this is obviously nonpositive, so -/1 - x + y/y^^2 < k2 = with k2=20 =3D 0 for example.  For 1 - x + y > 0, we have xy = converting=20 to /1 - x + y/y^^2 which is nonnegative and therefore /1 - x + = y/y^^2 >=20 =3D k2 with k2 =3D 0 again.  
 
Vickers'  criticism turned out to = be very=20 fortunate, not only for clarifying the typographical error and = avoiding the=20 wrong conclusion that I operated on only one side of an = inequality when=20 converting xy to the other form, but also in my developing = a detailed=20 argument concerning when the conversion from y/x to 1 - x + y becomes an = actual=20 function.   This occurs, for example, when y/x is a reduced=20 proper or improper fraction in the sense that numerator and=20 denominator have no common primes, in which case the unique = factorization into=20 primes and consideration of the three cases y/x > 1 and y/x < 1 = and y/x =3D=20 1 leads to the conclusion that the conversion is a function.  Thus, = on the=20 reduced rationals, we have a function.  This is not a bad set to = work with=20 mathematically, and certainly provides a nontrivial case where the = conversion is=20 a function and is accurate.
 
I hope that S. J. Vickers will continue = to=20 contribute to further discussion in this thread because of his = important=20 contributions, provided of course that he continues to emphasize = the=20 correction of errors and ways of further applying the = conversions.  If=20 somebody finds any further errors in my future writings, please give me = the=20 benefit of considering the possibility that I made a typographical=20 error.
 
Osher Doctorow   =20
------=_NextPart_000_000B_01BFED72.43157E80-- From rrosebru@mta.ca Tue Jul 25 10:08:52 2000 -0300 Received: (from Majordom@localhost) by mailserv.mta.ca (8.9.3/8.9.3) id KAA07720 for categories-list; Tue, 25 Jul 2000 10:05:07 -0300 (ADT) X-Authentication-Warning: mailserv.mta.ca: Majordom set sender to cat-dist@mta.ca using -f Date: Sun, 23 Jul 2000 23:12:56 +1000 (EST) From: maxk@maths.usyd.edu.au (Max Kelly) Message-Id: <200007231312.XAA05191@milan.maths.usyd.edu.au> To: categories@mta.ca, maxk@maths.usyd.edu.au Subject: categories: Como meeting CT2000 Sender: cat-dist@mta.ca Precedence: bulk Status: O X-Status: X-Keywords: X-UID: 16 I have just come from the meeting above, which was truly excellent, and led to a rich and valuable exchange of exciting new mathematics. It gives me great pleasure to express publicly my gratitute to Aurelio Carboni, Pino Rosolini,and Bob Walters for setting up and arranging, as the Organizing Committee, this international meeting, with all the manifold accompanying logistical problems. I must say that I found the lack of suitable blackboards an annoying if minor issue, since I am unused to preparing overhead transparencies, and was told two minutes before my talk that those I had prepared the night before were scarcely readable, in having too many lines to the page. In my disappointment and irritation , I used language stronger than I would have wished in criticising the lack of the usual communication-tools; I said "disgraceful" where "unfortunate" would have corresponded better to the situation. Thus I gave unintended offence to my three dear friends of the Organizing Committee. I now offer them my public apologies, and seek their pardon . Max Kelly. From rrosebru@mta.ca Tue Jul 25 10:08:55 2000 -0300 Received: (from Majordom@localhost) by mailserv.mta.ca (8.9.3/8.9.3) id KAA00526 for categories-list; Tue, 25 Jul 2000 10:02:18 -0300 (ADT) X-Authentication-Warning: mailserv.mta.ca: Majordom set sender to cat-dist@mta.ca using -f Message-ID: <001e01bff1f0$877ca080$1e7379a5@osherphd> From: "Osher Doctorow" To: Subject: categories: Re: Cross-Category "conversions" of some interest Date: Wed, 19 Jul 2000 19:15:38 -0700 MIME-Version: 1.0 Content-Type: multipart/alternative; boundary="----=_NextPart_000_001B_01BFF1B5.B93B2960" 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 Sender: cat-dist@mta.ca Precedence: bulk Status: O X-Status: X-Keywords: X-UID: 17 This is a multi-part message in MIME format. ------=_NextPart_000_001B_01BFF1B5.B93B2960 Content-Type: text/plain; charset="iso-8859-1" Content-Transfer-Encoding: quoted-printable From: Osher Doctorow osher@ix.netcom.com, Wed. July 19, 2000, 7:04PM A list member claims in a private communication to me that 3 things are = wrong with the x/y to 1 - x + y conversion. His first claim is that "it = does not ring true" that I meant to type k1 or k2. This criticism is = outside mathematics and has no meaning either there or in science. His second claim is that xy =3D (x/y)y^^2 works one way and (x/y)^^2 = (y^^3)/x works another way in the conversion and that the conversion of = / but not other operations is anyway of questionable validity. = Concerning the second part, the claim is meaningless. Since x/y is the = main "animal" in BCP and in Goguen/Product logic implication and both = have the form x/y, there is nothing to prevent me from comparing x/y = with 1 - x + y in order to compare BCP and Goguen/Product logic = implications with LBP and Lukaciewicz Logic. Concerning the first part, = we can define a conversion C_n which converts xy as a product of = (x/y)^^n g(x,y) where g(x,y) is a rational expression in powers of y = and/or x no part of which contains (x/y)^^m as a factor for 1 < =3D m < = =3D n and m, n are integers > =3D 1. C_n (C subscript n) for n =3D 1 = gives exactly my conversion, and the critic's objection case involves = C_2 which conversion is not being considered. The third argument is that the conversion restricted to x/y for x, y = coprime integers is alarming (because) continuity is lost (that is to = say, I should mention, that the rationals are not continuous while the = reals are) and because it is unclear how to apply the conversion to = expressions of the form xy (is xy to be the product of two coprime = integers or what?). This is really two objections except for the word = "alarming" which is not a word in mathematics or science. The first = objection, concerning continuity, implicitly assumes that the conversion = is required to be continuous. Although I used the conversion earlier to = attempt to convert xy in the Heisenberg Uncertainty Principle (HUP) xy > = k, which perhaps should "ideally" involve all real xy, if the critic = admits that the conversion works for rational x and y or even integer x = and y, then xy restricted to either rational or integer x and y converts = to two different inequalities depending on whether 1 - x + y < 0 or 1 - = x + y > 0 (respectively x > 1 + y or x < 1 + y), so the converted form = of xy does not obey the HUP, and therefore continuity is not even = required to show what I had attempted to show about the HUP. The second = objection, concerning whether xy is restricted to the product of two = coprime integers, is rather redundant considering the above. Yours truly, Osher Doctorow=20 ------=_NextPart_000_001B_01BFF1B5.B93B2960 Content-Type: text/html; charset="iso-8859-1" Content-Transfer-Encoding: quoted-printable
From: Osher Doctorow osher@ix.netcom.com, Wed. July = 19, 2000,=20 7:04PM
 

I am sending this again because of I typed "real" instead of = "integer" in one=20 place.

A list member claims in a private communication to me that 3 things = are wrong=20 with the x/y to 1 - x + y conversion. His first claim is that "it does = not ring=20 true" that I meant to type k1 or k2. This criticism is outside = mathematics and=20 has no meaning either there or in science.

His second claim is that xy =3D (x/y)y^^2 works one way and (x/y)^^2 = (y^^3)/x=20 works another way in the conversion and that the conversion of / but not = other=20 operations is anyway of questionable validity. Concerning the second = part, the=20 claim is meaningless. Since x/y is the main "animal" in BCP and in=20 Goguen/Product logic implication and both have the form x/y, there is = nothing to=20 prevent me from comparing x/y with 1 - x + y in order to compare BCP and = Goguen/Product logic implications with LBP and Lukaciewicz Logic. = Concerning the=20 first part, we can define a conversion C_n which converts xy as a = product of=20 (x/y)^^n g(x,y) where g(x,y) is a rational expression in powers of y = and/or x no=20 part of which contains (x/y)^^m as a factor for 1 < =3D m < =3D n = and m, n are=20 integers > =3D 1. C_n (C subscript n) for n =3D 1 gives exactly my = conversion,=20 and the critic’s objection case involves C_2 which conversion is = not being=20 considered.

The third argument is that the conversion restricted to x/y for x, y = coprime=20 integers is alarming (because) continuity is lost (that is to say, I = should=20 mention, that the rationals are not continuous while the reals are) and = because=20 it is unclear how to apply the conversion to expressions of the form xy = (is xy=20 to be the product of two coprime integers or what?). This is really two=20 objections except for the word "alarming" which is not a word in = mathematics or=20 science. The first objection, concerning continuity, implicitly assumes = that the=20 conversion is required to be continuous. Although I used the conversion = earlier=20 to attempt to convert xy in the Heisenberg Uncertainty Principle (HUP) = xy >=20 k, which perhaps should "ideally" involve all real xy, if the critic = admits that=20 the conversion works for rational x and y or even integer x and y, then = xy=20 restricted to either rational or integer x and y converts to two = different=20 inequalities depending on whether 1 - x + y < 0 or 1 - x + y > 0=20 (respectively x > 1 + y or x < 1 + y), so the converted form of xy = does=20 not obey the HUP, and therefore continuity is not even required to show = what I=20 had attempted to show about the HUP. The second objection, concerning = whether xy=20 is restricted to the product of two coprime integers, is rather = redundant=20 considering the above.

Yours truly,

Osher Doctorow

------=_NextPart_000_001B_01BFF1B5.B93B2960-- From rrosebru@mta.ca Tue Jul 25 10:09:08 2000 -0300 Received: (from Majordom@localhost) by mailserv.mta.ca (8.9.3/8.9.3) id KAA29536 for categories-list; Tue, 25 Jul 2000 10:07:27 -0300 (ADT) X-Authentication-Warning: mailserv.mta.ca: Majordom set sender to cat-dist@mta.ca using -f Date: Mon, 24 Jul 2000 09:56:23 -0500 (CDT) From: "Todd H. Trimble" Message-Id: <200007241456.JAA15586@fermat.math.luc.edu> To: categories@mta.ca Subject: query: presheaf construction Sender: cat-dist@mta.ca Precedence: bulk Status: O X-Status: X-Keywords: X-UID: 18 At the Como meeting last week, I asked various people a question which I view as having foundational significance: is there a setting in which one can iterate the presheaf construction (as free cocompletion) without ever having to use the word "small" or worry about size? Here is a more precise formulation of what I am after. I want an example of a compact closed bicategory B [think: bicategory of profunctors] with the following very strong property: the inclusion i: Ladj(B) --> B, of the bicategory of left adjoints in B, has a right biadjoint p such that, calling y: 1 --> pi the unit and e: ip -|-> 1 the counit, the isomorphisms which fill in the triangles iy yp i --> ipi p --> pip \ | \ | \ | ei \ | pe \| \| i p furnish the unit and counit, respectively, of adjunctions iy --| ei in B and pe --| yp in Ladj(B). (These structures should also be compatible with the symmetric monoidal bicategory structures on B and Ladj(B).) By exploiting compact closure, it's easy to see that p(b) is equivalent to an exponential (p1)^(b^op) in Ladj(B), where b^op denotes the dual of b in the sense of compact closure. So the unit y: 1 --> pi takes the yoneda-like form b --> v^(b^op); the axioms imply it is the fully faithful unit of a KZ-monad. The reactions I got were varied and interesting. As filtered through me, here are some (abbreviated) responses: (1) "No, I don't think there are any examples except the obvious locally posetal ones." (2) "The notion looks essentially algebraic, so I see no obstacle in principle to producing examples; it should even be easy for the right (2-categorically minded) people." (3) [From experts in domain theory] "Good question! Hmmmmmmmm....." (4) "It seems to me there is no reason in the world why examples should not exist, but the techniques developed for dealing with things like modest sets are probably not sufficient for dealing with your question, and may be misleading here." The various responses suggest *to me* that the question may be quite interesting and quite hard. My own sense, based on playing around with the axioms on a purely formal level, is that there is probably no inconsistency in the sense that any two 2-cells with common source and target are provably equal. My only vague idea on producing an example would be to proceed as Church and Rosser did in the old days: work purely syntactically, and consider the possibility of strong normalization for terms. Perhaps one could then show that the term model is not locally posetal. Todd From rrosebru@mta.ca Tue Jul 25 16:32:07 2000 -0300 Received: (from Majordom@localhost) by mailserv.mta.ca (8.9.3/8.9.3) id QAA11370 for categories-list; Tue, 25 Jul 2000 16:09:05 -0300 (ADT) X-Authentication-Warning: mailserv.mta.ca: Majordom set sender to cat-dist@mta.ca using -f To: concurrency@cwi.nl, categories@mta.ca Subject: categories: Preprint: Technical Report by Cattani, Leifer, and Milner Date: Tue, 25 Jul 2000 19:08:10 +0100 From: James Leifer Message-Id: Sender: cat-dist@mta.ca Precedence: bulk Status: RO X-Status: X-Keywords: X-UID: 20 The following paper: TITLE: Contexts and Embeddings for a Class of Action Graphs AUTHORS: Gian Luca Cattani, James J. Leifer, and Robin Milner is available as Technical Report 496, University of Cambridge Computer Laboratory. Copies may be obtained by sending email to: tech-reports@cl.cam.ac.uk or by downloading directly from these web addresses: http://www.cl.cam.ac.uk/users/glc25 http://www.cl.cam.ac.uk/users/jjl21 An abstract is attached below. -- G.L. Cattani, J.J. Leifer, and R. Milner. ABSTRACT: Action calculi, which have a graphical presentation, were introduced to develop a theory shared among different calculi for interactive systems. The pi-calculus, the lambda-calculus, Petri nets, the Ambient calculus and others may all be represented as action calculi. This paper develops a part of the shared theory. A recent paper by two of the authors was concerned with the notion of reactive system, essentially a category of process contexts whose behaviour is presented as a reduction relation. It was shown that one can, for any reactive system, uniformly derive a labelled transition system whose associated behavioural equivalence relations (e.g., trace equivalence or bisimilarity) will be congruential, under the condition that certain relative pushouts exist in the reactive system. In the present paper we treat closed, shallow action calculi (those with no free names and no nested actions) as a generic application of these results. We define a category of action graphs and embeddings, closely linked to a category of contexts which forms a reactive system. This connection is of independent interest; it also serves our present purpose, as it enables us to demonstrate that appropriate relative pushouts exist. Complemented by work to be reported elsewhere, this demonstration yields labelled transition systems with behavioural congruences for a substantial class of action calculi. We regard this work as a step towards comparable results for the full class. From rrosebru@mta.ca Wed Jul 26 10:34:10 2000 -0300 Received: (from Majordom@localhost) by mailserv.mta.ca (8.9.3/8.9.3) id KAA29898 for categories-list; Wed, 26 Jul 2000 10:29:06 -0300 (ADT) X-Authentication-Warning: mailserv.mta.ca: Majordom set sender to cat-dist@mta.ca using -f Message-ID: <397EE5A7.E17B9E4A@bangor.ac.uk> Date: Wed, 26 Jul 2000 14:20:40 +0100 From: Ronnie Brown X-Mailer: Mozilla 4.72 [en] (Win98; I) X-Accept-Language: en MIME-Version: 1.0 To: categories@mta.ca Subject: categories: Presentation Facilities at Conferences Content-Type: text/plain; charset=us-ascii Content-Transfer-Encoding: 7bit Sender: cat-dist@mta.ca Precedence: bulk Status: RO X-Status: X-Keywords: X-UID: 21 The following is suggested by Max Kelly's comments and some discussions at Como. We have to be prepared for the worst scenario, that blackboard facilities will get worse, and it may even get to a stage where conference administrators wonder why mathematicians are not using powerpoint and computer presentations like everyone else! People should be aware that Latex facilities for slides are good: just use \documentclass{slides} \begin{document} \raggedright \begin{slide} ......\end{slide} etc. A colleague here also got splendid results using the colour package (I need to investigate this!). I also like to use in the preamble \parindent=0pt \parskip=1ex and to use almost pidgin English, so that the impact is visual, with as few words as possible. What is not so clear is how to use say animated gif files in such a presentation. For this I have used a browser presentation using html files, and converting tex into html using tth http://hutchinson.belmont.ma.us/tth/ I hope this helps people. We could then ask conference centres to provide projection facilities, if these are a requirement of users. Ronnie Brown -- Prof R. Brown, School of Informatics, Mathematics Division, University of Wales, Bangor Dean St., Bangor, Gwynedd LL57 1UT, United Kingdom Tel. direct:+44 1248 382474|office: 382475 fax: +44 1248 361429 World Wide Web: home page: http://www.bangor.ac.uk/~mas010/ (Links to survey articles: Higher dimensional group theory Groupoids and crossed objects in algebraic topology) Symbolic Sculpture and Mathematics: http://www.bangor.ac.uk/SculMath/ Centre for the Popularisation of Mathematics http://www.bangor.ac.uk/cpm/ From rrosebru@mta.ca Wed Jul 26 16:23:38 2000 -0300 Received: (from Majordom@localhost) by mailserv.mta.ca (8.9.3/8.9.3) id QAA28841 for categories-list; Wed, 26 Jul 2000 16:21:25 -0300 (ADT) X-Authentication-Warning: triples.math.mcgill.ca: barr owned process doing -bs Date: Wed, 26 Jul 2000 14:02:20 -0400 (EDT) From: Michael Barr X-Sender: barr@triples.math.mcgill.ca To: categories@mta.ca Subject: categories: Re: Presentation Facilities at Conferences In-Reply-To: <397EE5A7.E17B9E4A@bangor.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: X-Keywords: X-UID: 22 I disagree. I think we should continue to protest the lack of blackboards. I have used transparencies and I have even used tex to prepare them. But I don't like it and I don't think it makes good talks and I don't see why we should acquiesce. Michael From rrosebru@mta.ca Thu Jul 27 20:48:17 2000 -0300 Received: (from Majordom@localhost) by mailserv.mta.ca (8.9.3/8.9.3) id UAA19443 for categories-list; Thu, 27 Jul 2000 20:41:57 -0300 (ADT) X-Authentication-Warning: mailserv.mta.ca: Majordom set sender to cat-dist@mta.ca using -f X-Originating-IP: [205.147.37.2] From: "Bill Halchin" To: categories@mta.ca Cc: bhalchin@hotmail.com Subject: categories: "free" poset question Date: Wed, 26 Jul 2000 23:19:33 GMT Mime-Version: 1.0 Content-Type: text/plain; format=flowed Message-ID: X-OriginalArrivalTime: 26 Jul 2000 23:19:33.0353 (UTC) FILETIME=[F4F44D90:01BFF757] Sender: cat-dist@mta.ca Precedence: bulk Status: O X-Status: X-Keywords: X-UID: 23 Hello Category Community, N (P, <=) ---------------------> (P/E, <=) \ | \ | \ | \ | \ | \ | g \ | f \ | \ | \ | \ | \ | \ | \ v (Q, <=) - This is a problem from Arbib's book on category theory - P is a pre-order - (P/E) and Q are posets - N and f are order-preserving functions from a pre-order to a poset. - g is a order-preserving function between posets P/E and G, i.e. a poset homomorphism, that is UNIQUE. - Question 1: we are building category where the objects are the collection of order-preserving functions from P to posets and morphisms are order-preserving functions between posets that make a diagram like the following commute, i.e. h.g = f Is the above statement true? h (P, <=) ---------------------> (R, <=) \ | \ | \ | \ | \ | \ | g \ | f \ | \ | \ | \ | \ | \ | \ v (Q, <=) - Question 2: if indeed this forms a category, then (P/E, N) is an initial object in this category. True?? - Question 3: the whole notion introduced by this Arbib problem is that of "free" poset, i.e. something very akin to a free algebra, free group, etc. I.e. the same kind of categoric construct. Yes???? Thank you, Bill Halchin ________________________________________________________________________ Get Your Private, Free E-mail from MSN Hotmail at http://www.hotmail.com From rrosebru@mta.ca Thu Jul 27 20:52:19 2000 -0300 Received: (from Majordom@localhost) by mailserv.mta.ca (8.9.3/8.9.3) id UAA15675 for categories-list; Thu, 27 Jul 2000 20:50:38 -0300 (ADT) X-Authentication-Warning: mailserv.mta.ca: Majordom set sender to cat-dist@mta.ca using -f Date: Wed, 26 Jul 2000 05:44:03 -0400 (EDT) From: Peter Freyd Message-Id: <200007260944.e6Q9i3a19367@saul.cis.upenn.edu> To: categories@mta.ca Subject: categories: Osher Doctorow Sender: cat-dist@mta.ca Precedence: bulk Status: O X-Status: X-Keywords: X-UID: 24 Bob: I've added a description of his dissertation, so use this if you haven't already sent the other out. I thought it might be interesting to find out about Osher Doctorow. Something called "Nupedia" lists him as one of its "very distinguished and active scholars, and all-around interesting people" to be found among its Editors and Peer Reviewers. Nupedia tells us: Osher Doctorow (PR) -- Ph.D. (1982 UCLA). Consultant in mathematics and physics mostly since 1973, Doctorow Consultants, Culver City, California. M.A. Mathematics (USC 1969), M.A. Anthropology (University of London 1961). Over 150 papers presented and publications, about 40 of which abstracted at Instititute for Logic at University of Vienna on the internet, plus (in addition to the 150 or so above) about 40 book reviews on math and physics mostly, at Amazon.com. Taught university mathematics five years; Staff Research Assistant (statistics) UCLA six years; Mathematician U.S. Defense Department 2-1/4 years in artificial satellites (Sustained Superior Performance Award in Mathematics 1984); Statistician at private research institute one year; High School/Middle school mathematics teacher two years. Member Armed Forces Communications and Electronics Association (AFCEA), UCLA Alumni Association (lifetime). Married 30+ years to Dr. Marleen Josie Doctorow (psychologist), one son, Eric. PsycINFO tells us: Author Doctorow, Osher. Institution U California, Los Angeles. Title Modeling cognitive growth by the linear system of linked differential equations (LSDE). Source Dissertation Abstracts International. Vol 43(10-A), Apr 1983, 3267. Key Phrase Identifiers linear system of differential equations, model of cognitive growth in reading & mathematics & language arts, 3rd graders, 4-5 yr longitudinal study Following the Nupedia lead we find that the "Abstract Service for Mathematical Logic" of the Institute for Logic at the University of Vienna lists abstracts for 45 journal publications for Doctorow, Osher. The journals in question turn out to be: 20 Doctorow Consultants Technical Report 5 Philosophy of Education Proceedings 3 HOPOS-L@LISTSERV.ND.EDU (History of Philosophy of Science) 3 Humanist Discussion Group, Center for Computing Group in Humanities, 3 Submitted for publication 2 MCRIT-L (Intl. Society on Multiple Criteria Decision Making) 2 Sociology and Social Research Vol. 48 Number 2 pp. 233-234 1 American Anthropologist, April 1963 1 Operations Research Society of America (ORSA) Newsletter 1 Orbis Scientiae Global Foundation Quanum Gravity Conference 17.12.1999 1 Policy Sciences 14 (1981), 31-47 1 Semigroups Archives 1 Socioeconomic Planning Sicences, 15(3), 1981 1 TCC 2000 Teaching in the Community Colleges Online Conference -- 45 Read the abstracts at www.logic.univie.ac.at/cgi-bin/abstract (where you can also find 13 abstracts by Cyrus F. Nourani). From rrosebru@mta.ca Thu Jul 27 20:53:11 2000 -0300 Received: (from Majordom@localhost) by mailserv.mta.ca (8.9.3/8.9.3) id UAA14936 for categories-list; Thu, 27 Jul 2000 20:51:30 -0300 (ADT) X-Authentication-Warning: mailserv.mta.ca: Majordom set sender to cat-dist@mta.ca using -f Message-Id: <3.0.6.32.20000726162640.0079cd80@pop.cwru.edu> X-Sender: cxm7@pop.cwru.edu X-Mailer: QUALCOMM Windows Eudora Light Version 3.0.6 (32) Date: Wed, 26 Jul 2000 16:26:40 -0500 To: categories@mta.ca From: Colin McLarty Subject: categories: Re: Presentation Facilities at Conferences In-Reply-To: References: <397EE5A7.E17B9E4A@bangor.ac.uk> 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 I agree with Mike Barr. I think there is a specific reason for using blackboards in math talks: Where most disciplines use graphics and texts to present data and conclusions, mathematicians often write to convey a line of reasoning as it develops. When I talk about math I often put formulas or diagrams on the board, and change them as I go. Slides and powerpoint can handle those changes in various ways, but none are as flexible or as graceful as writing on a board. Colin At 02:02 PM 7/26/00 -0400, Micheal Barr wrote: >I think we should continue to protest the lack of >blackboards. I have used transparencies and I have even used tex to >prepare them. But I don't like it and I don't think it makes good talks >and I don't see why we should acquiesce. > >Michael From rrosebru@mta.ca Fri Jul 28 12:47:13 2000 -0300 Received: (from Majordom@localhost) by mailserv.mta.ca (8.9.3/8.9.3) id MAA21735 for categories-list; Fri, 28 Jul 2000 12:43:54 -0300 (ADT) X-Authentication-Warning: mailserv.mta.ca: Majordom set sender to cat-dist@mta.ca using -f From: "Walter Tholen" Message-Id: <1000727110503.ZM218276@pascal.math.yorku.ca> Date: Thu, 27 Jul 2000 11:05:03 -0400 X-Mailer: Z-Mail (4.0.1 13Jan97) To: categories@mta.ca Subject: categories: AMS SS J1 (Applied Categorical Structures) in Toronto Cc: tholen@pascal.math.yorku.ca 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: 26 Below you will find the final schedule for the Special Session on "Applied Categorical Structures" at the up-coming AMS Meeting in Toronto, Sept. 23&24. There will be a Welcome Party on Friday evening (Sept. 22) - details to be communicated in early September. Note specifically that the program on Sunday afternoon continues until 5 pm rather than until 4pm as previously announced. For comprehensive and continually updated meeting and program information, including accommodation in Toronto, see http://www.ams.org/meetings/ Hotel accomodation in Toronto during the month of September can be very tight. In fact, the deadlines for making bookings in the two AMS-recommended hotels in Toronto are approaching rapidly. These are: "Courtyard by Marriott", 475 Yonge St., (416) 924-0611, $182 (Can.) for single or double by August 1; "Days Inn", 30 Carlton St., (416) 977-6655 or (800) 325-2525, $139 (Can.) for single or double by August 23. As an alternative to the Days Inn (same price or lower, 15 min walk to conference site) you may want to try the following smaller downtown hotel, which we have used for vistors in the past: Howard Johnson Inn, 89 Avenue Road, (416) 964-1220 or (800) 446 4656. We look forward to seeing you in Toronto. Joan Wick Pelletier Walter Tholen Saturday, Sept. 23: 9:00 Andre Joyal 3:00 Stephen Awodey 9:30 Myles Tierney 3:30 Lars Birkedal 10:00 Jack Duskin 4:00 David Benson 10:30 Marco Grandis 4:30 John MacDonald 11:00 Enrico Vitale 5:00 Richard Wood Sunday, Sept. 24: 9:00 Marta Bunge 2:00 Joachim Lambek 9:30 Michael Makkai 2:30 James Madden 10:00 Robin Cockett 3:00 Gloria Tashjian 10:30 M. M. Mawanda 3:30 Robert Pare 11:00 F. William Lawvere 4:00 Jiri Rosicky 4:30 F. J. O. Souza All talks are 25 minutes long. The titles follow. The full abstracts may be seen at the web site cited above. Abstract # Title Authors Date Received 957-18-265 On the pivotal, symmetric case of involutory Hopf 13-jul-2000 objects. Fernando J. O. Souza*, fernando@math.uic.edu 957-18-235 Higher category theory. 12-jul-2000 Andre Joyal*, joyal@math.uqam.ca 957-06-218 Injective hulls of partially ordered monoids. 12-jul-2000 J. Lambek* 957-18-214 Modelling a sketch in an object in a 2-category. 11-jul-2000 Michael Johnson, mike@ics.mq.edu.au Robert Rosebrugh, rrosebru@mta.ca R. J. Wood*, rjwood@mathstat.dal.ca 957-18-204 Open problems on finiteness and their counting 11-jul-2000 measures. Mbila-Mambu Mawanda*, mm.mawanda@nul.ls 957-18-199 Monoreflections in categories of ordered rings. 10-jul-2000 James J Madden*, madden@math.lsu.edu 957-18-198 Nerves of Bicategories: Morphisms and Simplicial 10-jul-2000 Maps. John W Duskin*, duskin@math.buffalo.edu 957-18-157 A summary report on the state of our knowledge of 05-jul-2000 weak higher dimensional categories. Michael Makkai*, makkai@math.mcgill.ca 957-18-140 Dominances and Spread Completions. 04-jul-2000 Marta C Bunge*, bunge@math.mcgill.ca 957-18-132 Finitely productive classes of uniform spaces 03-jul-2000 which generate cartesian-closed categories. Gloria Tashjian* 957-68-123 Certain spans of sketches model problems of 29-jun-2000 complexity NP. David B Benson*, dbenson@eecs.wsu.edu 957-18-107 Flat covers and factorizations. 27-jun-2000 Jiri Rosicky*, rosicky@math.muni.cz 957-18-90 Free Double Categories and the Word Problem for 25-jun-2000 Groups. Robert Par\'e*, pare@mscs.dal.ca Robert MacG. Dawson, rdawson@husky1.stmarys.ca 957-18-77 A higher dimensional homotopy sequence. 22-jun-2000 Marco Grandis, grandis@dima.unige.it Enrico Vitale*, vitale@agel.ucl.ac.be 957-18-76 Some absolute pullbacks and pushouts in 22-jun-2000 $\boldsymbol{\Delta}$. Myles Tierney*, tierney@math.rutgers.edu 957-18-61 Monads and Structure. 16-jun-2000 John L. MacDonald*, johnm@math.ubc.ca 957-18-59 Relating realizability using sheaves. 16-jun-2000 Steve Awodey*, awodey@cmu.edu Andrej Bauer Dana S Scott 957-03-51 Relative and Modified Relative Realizability. 13-jun-2000 Lars Birkedal*, birkedal@itu.dk Jaap van Oosten, jvoosten@math.uu.nl 957-18-39 Higher fundamental functors in some categories of 07-jun-2000 presheaves. Marco Grandis*, grandis@dima.unige.it 957-18-30 Game theory revisited: categorical proof theories 31-may-2000 for games. J. Robin B. Cockett*, robin@cpsc.ucalgary.ca 957-18-19 Toposes and Continuum Microphysics. 22-may-2000 F. William Lawvere*, wlawvere@acsu.buffalo. From rrosebru@mta.ca Fri Jul 28 12:58:13 2000 -0300 Received: (from Majordom@localhost) by mailserv.mta.ca (8.9.3/8.9.3) id MAA25319 for categories-list; Fri, 28 Jul 2000 12:56:41 -0300 (ADT) X-Authentication-Warning: mailserv.mta.ca: Majordom set sender to cat-dist@mta.ca using -f Date: Fri, 28 Jul 2000 04:46:34 -0400 (EDT) From: Peter Freyd Message-Id: <200007280846.e6S8kXa06335@saul.cis.upenn.edu> To: categories@mta.ca Subject: categories: blackboards at Como Sender: cat-dist@mta.ca Precedence: bulk Status: O X-Status: X-Keywords: X-UID: 27 [NOTE FROM MODERATOR: This message should be the last of the discussion on this issue, regards to all, Bob Rosebrugh] The posts from Mike and Colin prompt me to go on record. In my talk at Como I did not use projectors. I used the two blackboards that were provided by the organizers. From rrosebru@mta.ca Fri Jul 28 13:21:44 2000 -0300 Received: (from Majordom@localhost) by mailserv.mta.ca (8.9.3/8.9.3) id NAA22148 for categories-list; Fri, 28 Jul 2000 13:20:05 -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 (8.9.3/8.9.3) with SMTP id BAA13769 for ; Fri, 28 Jul 2000 01:32:10 -0300 (ADT) X-Received: FROM siv.maths.usyd.edu.au BY zent.mta.ca ; Fri Jul 28 01:28:15 2000 -0300 X-Received: from smap@localhost by siv.maths.usyd.edu.au (8.8.8/5.7 to SMTP) id OAA51146; Fri, 28 Jul 2000 14:31:10 +1000 (EST) X-Received: from milan.maths.usyd.edu.au (stevel(.pmstaff;2406.2002)@milan.maths.usyd.edu.au) [129.78.69.163] by siv.maths.usyd.edu.au via smtpdoor V12.2 id 65627; Fri, 28 Jul 2000 14:31:10 +1000 X-Received: from stevel@localhost by milan.maths.usyd.edu.au (8.8.8/5.5 to SMTP) id OAA20723; Fri, 28 Jul 2000 14:31:10 +1000 (EST) From: Steve Lack MIME-Version: 1.0 Content-Type: text/plain; charset=us-ascii Content-Transfer-Encoding: 7bit Message-ID: <14721.3214.251484.82809@milan.maths.usyd.edu.au> Date: Fri, 28 Jul 2000 14:31:10 +1000 (EST) To: categories@mta.ca Subject: categories: re: query: presheaf construction In-Reply-To: <200007241456.JAA15586@fermat.math.luc.edu> References: <200007241456.JAA15586@fermat.math.luc.edu> X-Mailer: VM 6.71 under 21.1 (patch 7) "Biscayne" XEmacs Lucid Sender: cat-dist@mta.ca Precedence: bulk Status: RO X-Status: X-Keywords: X-UID: 28 How about Span? Steve Lack. > At the Como meeting last week, I asked various people a question > which I view as having foundational significance: is there a > setting in which one can iterate the presheaf construction (as > free cocompletion) without ever having to use the word "small" > or worry about size? > > Here is a more precise formulation of what I am after. > I want an example of a compact closed bicategory B [think: > bicategory of profunctors] with the following very strong > property: the inclusion > > i: Ladj(B) --> B, > > of the bicategory of left adjoints in B, has a right biadjoint p > such that, calling y: 1 --> pi the unit and e: ip -|-> 1 the counit, > the isomorphisms which fill in the triangles > iy yp > i --> ipi p --> pip > \ | \ | > \ | ei \ | pe > \| \| > i p > > furnish the unit and counit, respectively, of adjunctions iy --| ei > in B and pe --| yp in Ladj(B). (These structures should also be > compatible with the symmetric monoidal bicategory structures on > B and Ladj(B).) By exploiting compact closure, it's easy to see > that p(b) is equivalent to an exponential (p1)^(b^op) in Ladj(B), > where b^op denotes the dual of b in the sense of compact closure. > So the unit y: 1 --> pi takes the yoneda-like form b --> v^(b^op); > the axioms imply it is the fully faithful unit of a KZ-monad. > > The reactions I got were varied and interesting. As filtered through > me, here are some (abbreviated) responses: > > (1) "No, I don't think there are any examples except the obvious > locally posetal ones." > (2) "The notion looks essentially algebraic, so I see no obstacle > in principle to producing examples; it should even be easy for > the right (2-categorically minded) people." > (3) [From experts in domain theory] "Good question! Hmmmmmmmm....." > (4) "It seems to me there is no reason in the world why examples > should not exist, but the techniques developed for dealing > with things like modest sets are probably not sufficient for > dealing with your question, and may be misleading here." > > The various responses suggest *to me* that the question may be > quite interesting and quite hard. > > My own sense, based on playing around with the axioms on a purely > formal level, is that there is probably no inconsistency in the sense > that any two 2-cells with common source and target are provably equal. > My only vague idea on producing an example would be to proceed as Church > and Rosser did in the old days: work purely syntactically, and consider > the possibility of strong normalization for terms. Perhaps one could > then show that the term model is not locally posetal. > > Todd > From rrosebru@mta.ca Sat Jul 29 09:42:55 2000 -0300 Received: (from Majordom@localhost) by mailserv.mta.ca (8.9.3/8.9.3) id JAA27230 for categories-list; Sat, 29 Jul 2000 09:37:19 -0300 (ADT) X-Authentication-Warning: mailserv.mta.ca: Majordom set sender to cat-dist@mta.ca using -f Date: Sat, 29 Jul 2000 06:57:56 -0500 (CDT) Subject: categories: re: query: presheaf construction From: "Todd H. Trimble" Message-Id: <200007291157.GAA26395@fermat.math.luc.edu> To: categories@mta.ca Sender: cat-dist@mta.ca Precedence: bulk Status: O X-Status: X-Keywords: X-UID: 29 > How about Span? > > Steve Lack. > Since Ladj(Span) is essentially Set, we would need, for every set b, a set pb such that for every a, the large category of spans a -|-> b is equivalent to the small discrete category of functions a --> pb. This doesn't work. [Just to avoid a possible misunderstanding: if B is a bicategory, then by Ladj(B) I mean the locally full subbicategory of B with the same objects as B and whose 1-cells are left adjoints in B. Katis and Walters have a paper which uses the same notation Ladj(B) for something else.] -- Todd. >> At the Como meeting last week, I asked various people a question >> which I view as having foundational significance: is there a >> setting in which one can iterate the presheaf construction (as >> free cocompletion) without ever having to use the word "small" >> or worry about size? >> >> Here is a more precise formulation of what I am after. >> I want an example of a compact closed bicategory B [think: >> bicategory of profunctors] with the following very strong >> property: the inclusion >> >> i: Ladj(B) --> B, >> >> of the bicategory of left adjoints in B, has a right biadjoint p >> such that, calling y: 1 --> pi the unit and e: ip -|-> 1 the counit, >> the isomorphisms which fill in the triangles >> iy yp >> i --> ipi p --> pip >> \ | \ | >> \ | ei \ | pe >> \| \| >> i p >> >> furnish the unit and counit, respectively, of adjunctions iy --| ei >> in B and pe --| yp in Ladj(B). (These structures should also be >> compatible with the symmetric monoidal bicategory structures on >> B and Ladj(B).) By exploiting compact closure, it's easy to see >> that p(b) is equivalent to an exponential (p1)^(b^op) in Ladj(B), >> where b^op denotes the dual of b in the sense of compact closure. >> So the unit y: 1 --> pi takes the yoneda-like form b --> v^(b^op); >> the axioms imply it is the fully faithful unit of a KZ-monad. >> [rest of message snipped] From rrosebru@mta.ca Mon Jul 31 09:31:33 2000 -0300 Received: (from Majordom@localhost) by mailserv.mta.ca (8.9.3/8.9.3) id JAA28800 for categories-list; Mon, 31 Jul 2000 09:26:07 -0300 (ADT) X-Authentication-Warning: mailserv.mta.ca: Majordom set sender to cat-dist@mta.ca using -f Date: Sun, 30 Jul 2000 21:03:41 -0400 (EDT) From: F W Lawvere Reply-To: wlawvere@ACSU.Buffalo.EDU To: categories@mta.ca Subject: categories: Como Meeting 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: 30 Last week's CT 2000 meeting in Como, Italy had two quite notable features, which augur well for the future of category theory: - the significant number of young people who are actively learning and developing category theory and who presented their new results; - the unusual number of senior researchers in other fields whose essential use of category theory was demonstrated in their interesting lectures. Congratulations to the organizers, as well as to the scientific committee, and thanks for their hard work which successfully brought us all together. ***************************************************************** F. William Lawvere Mathematics Dept. SUNY Buffalo, Buffalo, NY 14214, USA 716-829-2144 ext. 117 HOMEPAGE: http://www.acsu.buffalo.edu/~wlawvere ***************************************************************** From rrosebru@mta.ca Mon Jul 31 20:39:13 2000 -0300 Received: (from Majordom@localhost) by mailserv.mta.ca (8.9.3/8.9.3) id UAA31399 for categories-list; Mon, 31 Jul 2000 20:38:00 -0300 (ADT) X-Authentication-Warning: mailserv.mta.ca: Majordom set sender to cat-dist@mta.ca using -f Date: Mon, 31 Jul 2000 11:44:45 -0400 (EDT) From: Peter Freyd Message-Id: <200007311544.e6VFijI18118@saul.cis.upenn.edu> To: categories@mta.ca Subject: categories: Reality check Sender: cat-dist@mta.ca Precedence: bulk Status: O X-Status: X-Keywords: X-UID: 31 In an earlier posting I showed how to define co-inductively the closed interval, in particular I showed that its elements are named by sequences of 0s and 1s with the usual binary-expansion equivalence relation. There is a well-known computational problem with this approach, already in the definition of the midpoint operation: at what point can you determine the first digit of the midpoint of .0000... and .1111...? At the Como meeting I learned from Andrej Bauer about a better approach. Take the elements of [-1,1] to be named by infinite sequences of _signed_ binary digits, that is -1, 0, +1. [Just to confuse matters, Scedrov and I once used signed _ternary_ digits (n Cats and Allegators for the "Freyd curve"). The signed binary expansions .+1 -1 and .0 +1 describe the same number, to wit, 1/4.] Using signed binary expansions one can compute midpoints with a little 3-state machine that takes as input the sequence of pairs of signed binary digits of the given numbers x and y, and produces as output a sequence of signed binary digits for the midpoint x|y. (There may, indeed, be momentary delays in the output, but there will not be an indefinite delay -- indeed, the number of output digits will never be more than one less than the number of pairs of input digits). The challenge is to revise the co-induction so that it is this better version that emerges. In the previous version I worked in the category of posets with _distinct_ top and bottom, that is, those posets for which not[(B = x) and (x = T)]. In the revised version I'll strengthen the condition by working in the category of posets with _separated_ top and bottom: [(B < x) or (x < T)]. (The conditions are equivalent in the presence of De Morgan's law. In a topos the top and bottom of omega are always distinct but they are separated only when De Morgan's law is satisfied throughout.) In the previous setting I defined what I'll now call the _thin_ version of the ordered-wedge of X and Y, to wit, the set of pairs, satisfying the condition: (x = T) or (B = y). The _thick_ version is the set of pairs, satisfying the two weaker conditions: (x < T) => (B = y) (B < y) => (x = T) (each of which is classically equivalent to the single condition used in the thin version). Easy exercise: if top and bottom are separated in X and Y, then they are separated in the thick version of the ordered-wedge XvY. (Indeed, it's enough for top and bottom to be separated in just one of X and Y . No, it is not enough to assume just that they are distinct in each.) A map X -> XvX is thus given by a pair d,u: X -> X such that for all x: (dx < T) => (B = ux) (B < ux) => (dx = T) The final coalgebra for XvX is still the closed interval, but now in the better computational sense. Let me explain. Given an arbitrary coalgebra d,u : X -> X, I need to describe a coalgebra homomorphism f: X -> I. where I is the set of equivalence types of infinite sequences of signed binary digits. The first step is to work not with elements of X but elements of XvX. Consider a machine that given :XvX asks in parallel the questions: "B < y?" "B < ux and dy < T?" "x < T?" Exercise: If the top and bottom of X are separated and d,u describe a map to the thick ordered-wedge XvX, then at least one of these questions has a positive answer. Given z:X obtain a sequence of signed binary digits by starting with the pair = and iterating the non-deterministic procedure: If B < y then emit +1 as output and replace with ; If B < ux and dy < T then emit 0 as output and replace with ; If x < B then emit -1 as output and replace with . Not-so-easy exercises: regardless of the non-determinism, the element fz:[-1,+1] named by the resulting sequence is determined. Moreover, f(uz) = u(fz) and f(dz) = df(z). PS. There is some geometry behind this stuff. Let me here mention just this: given a pair in XvX map it into the four-fold ordered-wedge XvXvXvX. Think of each of the four copies of X as one "quarter" of the whole. If B < y then the point lies inside the "top half" (the 3rd and 4th quarters). If B < ux and dy < T then the point lies inside the "middle half" (the 2nd and 3rd quarters). If x < B then the point lies inside the bottom half" (the 1st and 2nd quarters). Clearly any point is inside at least one of these three halves. The output-digit registers which of the three halves is moved to and the corresponding pair-replacement effects that move. PPS. On 22 Dec I gave a Dedekind-cut proof that the interval [0,1] constructed in the standard fashion from (unsigned) binary sequences is the final coalgebra for the functor that sends X (with distinct top and bottom) to the thin version of XvX. That proof should be replaced. First note that the midpoint-algebra homomorphism from [0,1] to [-1,1] can be effected simply by replacing each 0 with -1 and keeping each 1 as +1. Given d,u:X -> X such that for all x it is the case that either dx = T or ux = B , consider a machine that upon given x:X asks in parallel the questions "dx = T?" and "ux = B?". If dx = T then emit +1 as output and replace x with ux, If ux = B then emit -1 as output and replace x with dx. Given x:X one may iterate this (non-deterministic) procedure to obtain a sequence of +1s and -1s. Pretty-easy exercises: regardless of the non-determinism, the element fx:[-1,+1] named by the resulting sequence is determined; f(ux) = u(fx); f(dx) = df(x).