Geometry.Net - Pure_And_Applied_Math: Category Theory

SUO: Category Theory
SUO category theory. Third thought tells me that we probably can't do a goodjob of this without doing a bit of spadework in category theory first.
http://suo.ieee.org/email/msg09002.html

Extractions: Thread Links Date Links Thread Prev Thread Next Thread Index Date Prev ... Date Index SUO: Re: Category Theory From: Prev by Date: SUO: Re: Category Theory Next by Date: SUO: Re: CG: Question about CGs and OO concepts Prev by thread: RE: SUO: CG representations for WordNet Next by thread: SUO: Re: Category Theory Index(es): Date Thread
Functional Programming Archive (monads And Category Theory)
functional programming archive. monads and category theory subject area. KeywordsMonads; category theory; Kleisli triple; Imperative functional programming.
http://www.dcs.qmul.ac.uk/SEL-HPC/Articles/GeneratedHtml/functional.monads.html

Extractions: A BibTeX version of this database can be found here . Article links with a size in kbytes next to them are correct; documents without a size havn't been checked yet. This document was automatically generated on Tue Jun 25 2:00:42 2002 . Webmaster , Department of Computer Science, QMW, London University E Moggi "Computational lambda-calculus and monads" In Proceedings of the Logic in Computer Science Conference bibtex 20.8 kbytes dvi paper E Moggi "An Abstract View of Programming Languages" ,Technical report ECS-LFCS-90-113, Dept. of Computer Science, Edinburgh Univ., 90. bibtex 63.3 kbytes dvi paper Jonathan M. D. Hill , and Keith Clarke "An introduction to category theory, category theory monads, and their relationship to functional programming" bibtex html abstract 59.1 kbytes postscript paper Keywords: Monads; Category theory; Kleisli triple; Imperative functional programming Francoise Bellegarde , and James Hook "Monads, Indexes, and Transformations" ,Technical report CS-94-008, Oregon Graduate Institute CS, 94.
MATHS: Category Theory
category theory. Motivation. category theory is a way for talking about the relationshipsbetween the classes of objects modeled by mathematics and logic.
http://www.csci.csusb.edu/dick/maths/math_25_Categories.html

Extractions: CSUSB CompSci Dick Botting MATHS ... Notation Category Theory is a way for talking about the relationships between the classes of objects modeled by mathematics and logic. It is a model of a collection of things with some structural similarity. It is a comparatively recent abstraction from the various abstract algebras developed in the early part of the 20th century. The original use of the term category was in the idea of a 'categorical' axiom system - an axiom system which defined its objects so exactly that all objects that satisfied the axioms were isomorphic - they mapped into each other, one-to-one, preserving all the axioms and structure. This is important, because if a logic is categorical and there exists a simple (or cheaply implemented) example then that model can become the standard and all others are handled in terms of this standard. For example binary numbers have all the properties that one can expect of objects that satisfy the rules that describe a "natural number" and are cheap to emulate using electronics. The name for such ideal systems has been changed several times in this century - categorical, free, universal, initial,... Many times category theorists have discovered that some results that they have uncovered have been discovered within a totally different area - say the theory of languages and automata. Equally often an enterprising researcher in mathematics of computer science has found that category theory allowed them to express a speicific property they had observed in more general terms. The more general veiw then leads to shorter and simpler proofs of more results. This in turn often illuminates other problems.
Citations: Category Theory For Computing Science - Barr, Wells (ResearchIndex)
Barr, M., Wells, C. 1990. category theory for Computing Science. PrenticeHall. category theory for Computing Science. Prentice Hall, 1989.
http://citeseer.nj.nec.com/context/1728/0

Extractions: Expressive Logics for Coalgebras via Terminal Sequence Induction - Pattinson (Correct) ....of relators in a coalgebraic setting. The extension of endofunctors to relations is an integral part of Moss de nition of the semantics of coalgebraic logic, which is given in terms of initial algebras. For the basic notions regarding (initial) algebras we refer to the book by Barr and Wells De nition 5.3. Suppose M. Barr and C. Wells. Category Theory for Computing Science . Prentice Hall, 1989. Electronic Notes in Theoretical Computer Science 61(2001) - Url Http Www (Correct) ....(iii) denoting G (s; t; k) s ; t ; k ) s (s) t (t) and k =G(s)k (compatibility for foreign keys) In the sequel, when the component of G is obvious, we will omit the superscript. Evidently , morphisms of database schemes form a category which we denote DbSch.
Category Theory
category theory. I am reminded of a friend's account of his category theory lecturewhich began with, We will now consider the class of 'stuff'. BillTozier.
http://c2.com/cgi/wiki?CategoryTheory
Mathematics Online Compendium: Category Theory
category theory, homological algebra http//www.math.niu.edu/~rusin/knownmath/index/18-XX.htmlApplied and Computational category theory at RISC-Linz http
http://www.dei.unipd.it/~cuzzolin/MOCcategory.html
International Category Theory Meeting
International category theory Meeting (CT97), UBC, Vancouver, July1319, 1997. Organizer John MacDonald. One of the founders of
http://www.pims.math.ca/activities/exthem97.2.html

Extractions: Organizer: John MacDonald One of the founders of the subject, Saunders MacLane gave the keynote address. These meetings take place in the Pacific Northwest for the first time. They have not been held in the Pacific region since the MSRI meetings in 1993. Scientific program: There were 45 talks from all areas of the subject, including applications to computer science, algebra and foundations. The participants are nearly all mathematicians or computer scientists and come from 22 countries. Speakers: Saunders Mac Lane: The Scope of Category Theory Michael Barr: Some questions-and some answers-on *-autonomous categories Heinrich Kleisli: The chu *-algebra of a group Susan Niefield: A Skeletal Topos of Finite Sets: Implementing Finite Structures in Mathematica Robert Dawson: When can a double diagram be composed? John MacDonald: Distributivities and Liftings Art Stone: Soft adjunctions: stacking cubes, co-existence
Introduction To Category Theory
Introduction to category theory. Graham Hutton School of Computer Scienceand IT University of Nottingham. category theory is a mathematical
http://www.cs.nott.ac.uk/~gmh/categories.html

Extractions: Category theory is a mathematical approach to the study of algebraic structure that has become an important tool in theoretical computing science, particularly for semantics-based research. The aim of this course is to teach the basics of category theory, in a way that is accessible and relevant to computer scientists. The emphasis is on gaining a good understanding the basic definitions, examples, and techniques, so that students are equipped for further study on their own of more advanced topics if required. The course comprises five 90-minute lectures, each with exercises Categories (what is category theory, why is it useful, why is it useful to computing, course topics, graphs, labelled graphs, categories, examples of categories); Functors (graph homomorphisms, labelled graph homomorphisms, functors, examples of functors, functors as arrows, functors with two arguments); Natural transformations (commuting diagrams, natural transformations, natural transformations as arrows, the Godement calculus);
TOPOLOGY And CATEGORY THEORY SITES
TOPOLOGY and category theory SITES. Topology Atlas Topology Atlas Questionsin Topology Ask a Topologist Bulletin Board Topology Atlas Commentary
http://www.csupomona.edu/~hlord/topcat.html
Humanist Archives Vol. 2: "category Theory" And More (22)
category theory and more (22). I have held it in my hands long enough to knowthat it contains very much more than a discussion of 'category theory'.
http://lists.village.virginia.edu/lists_archive/Humanist/v02/0314.html
Prospects For Category Theory In Aldor
Prospects for category theory in Aldor. Saul Youssef, Categorical Programming LanguagesWorkshop, University of Western Ontario, London, Canada, July, 2001.
http://nut.bu.edu/~youssef/papers/math/aldor/
Constructive Category Theory
Constructive category theory. See URL http//pauillac.inria.fr/~saibi/ Download(archive compatible with Coq V7.4). Author Amokrane Saïbi. Institution INRIA.
http://coq.inria.fr/contribs/category.html
Lambda The Ultimate Category Theory For Non-mathematicians
category theory for nonmathematicians. category theory for non-mathematiciansstarted 8/20/01; 14822 PM - last post 8/27/01; 20414 AM.
http://lambda.weblogs.com/discuss/msgReader$1696

Extractions: 8/21/01; 12:56:54 AM (reads: 1206, responses: 0) Are there any books in which programming and the math (category theory) are developed in parallel? Like a book on category theory with actual ML code? All the books I've seen are either pure abstract math (i.e. theorem / proof) or functional programming with at most a cursory reference to category theory, like "A fold function is a catamorphism." Also is there any glossary out there that relates different language constructs and category theory terminology? Like "Monad" seems to be strongly attached to Haskell and the writings of Wadler. Never seen "Monad" in CAML code. Monads seem to have a parallel in Scheme closures, but I've never seen anyone make this analogy. Cheers
Category Theory Bulletin Board
category theory Bulletin Board. To types, logic; Subject category theoryBulletin Board; From RROSEBRUGH RROSEBRUGH%MTA.BITNET@mitvma.mit.edu ;
http://www.cis.upenn.edu/~bcpierce/types/archives/1990/msg00014.html

Extractions: [Prev] [Next] [Index] [Thread] To : types, logic Subject : Category Theory Bulletin Board From RROSEBRUGH%MTA.BITNET@mitvma.mit.edu Date : Tue, 13 Mar 90 11:18:45 EST Sender meyer@theory.lcs.mit.edu Prev: Yet another talk on OO prog Next: Decision problems for propositional linear logic Index(es): Main Thread
Conference On CATEGORY THEORY AND COMPUTER SCIENCE
Conference on category theory AND COMPUTER SCIENCE. The main purpose of theseconferences is to link research in category theory with computer science.
http://www.cis.upenn.edu/~bcpierce/types/archives/1990/msg00026.html

Extractions: [Prev] [Next] [Index] [Thread] To : types, logic, concurrency Subject : Conference on CATEGORY THEORY AND COMPUTER SCIENCE From curien%FRULM63.BITNET@mitvma.mit.edu (Pierre-Louis Curien) Date : Fri, 4 May 90 01:44:58 EDT Sender meyer@theory.lcs.mit.edu Prev: LICS '90, EARLY REGISTRATION DEADLINE Next: On confluence of simply typed Beta Index(es): Main Thread
M584: Category Theory
Mathematics 584 category theory. Instructor Jonathan Smith, 496 Carver, 48172(voice mail). e-mail jdhsmithATmathDOTiastateDOTedu (substitute punctuation).
http://www.math.iastate.edu/jdhsmith/class/M584F02.htm

Extractions: http://www.lib.iastate.edu/cgi-bin/isuauth.pl?File=f02list/math584smith.html Study plan: reserve 1 - 2 hours for homework between each pair of classes. Successful performance in the class depends critically on completion of the homework assignments. Syllabus: Chapters I - IV 8/28 for 9/4: Show that id : Ob( C Mor( C ) is 1-1.
Category Theory And Consciousness
category theory and consciousness. Matti Pitkänen. Abstract. Goro Katohas proposed an ontology of consciousness relying on category theory.
http://www.physics.helsinki.fi/~matpitka/articles/acategory.html

Extractions: http://www.physics.helsinki.fi/~matpitka Abstract Goro Kato has proposed an ontology of consciousness relying on category theory. Category theory has been proposed as a new approach to the deep problems of modern physics, in particular quantization of General Relativity. Category theory might provide the desired systematic approach to fuse together the bundles of general ideas related to the construction of the configuration space geometry using a generalization of the quantum holography principle and to the construction of configuration space spinor fields and of S-matrix. Category theory might also have natural applications in the general theory of consciousness and the theory of cognitive representations. One can indeed imagine several applications of the category theory to TGD inspired theory of consciousness: a) Cognition is categorizing and category theory suggests itself as a tool for understanding cognition and self hierarchies and the abstraction processes involved with conscious experience.
Coherence In Category Theory And The Church-Rosser Property
Coherence in category theory and the ChurchRosser Property. C. BarryJay Abstract Szabo's derivation systems on sequent calculi
http://www.lfcs.informatics.ed.ac.uk/reports/91/ECS-LFCS-91-181/
Calgary Peripatetic Research Group On Logic And Category Theory
Calgary Peripatetic Research Group on Logic and category theory. Meetingson Logic and category theory to be held in the Philosophy
http://pages.cpsc.ucalgary.ca/~danaha/CPRGLCT/CPRGLCT.html
EServer TC Library: Articles>Rhetoric>Theory
sort by author, McLeod, Susan H. JAC (1991). Articles Rhetoric theory.
http://tc.eserver.org/dir/Articles/Rhetoric/Theory

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