21. ATCAT Dalhousie University, Halifax. Weekly meetings.Category Science Math Algebra category theory Research Groups......@CAT. @CAT (Atlantic category theory Seminar) is our weekly seminar in which topicsrelated to category theory (algebra, logic, topology, category theory itself http://www.mscs.dal.ca/~pare/atcat.html

@CAT @CAT ( At lantic Cat egory Theory Seminar) is our weekly seminar in which topics related to category theory (algebra, logic, topology, category theory itself, etc.) are discussed. We meet on Tuesdays, starting at 2:30. Everyone is welcome. If you wish to be put on the mailing list, contact me at pare@mscs.cs.dal.ca 2002-2003 Participants List of talks Upcoming talks The Naming of Cats - T.S.Elliot

22. Category Theory - Wikipedia category theory. From Wikipedia, the free encyclopedia. Category This isthe Gelfand representation. History of category theory. Categories http://www.wikipedia.org/wiki/Category_theory

Main Page Recent changes Edit this page Older versions Special pages Set my user preferences My watchlist Recently updated pages Upload image files Image list Registered users Site statistics Random article Orphaned articles Orphaned images Popular articles Most wanted articles Short articles Long articles Newly created articles All pages by title Blocked IP addresses Maintenance page External book sources Printable version Talk Log in Help Category theory From Wikipedia, the free encyclopedia. Category theory is a mathematical theory that deals in an abstract way with mathematical structures and relationships between them. Although originally developed in the context of algebraic geometry algebraic topology and universal algebra , it is now also used in various other branches of mathematics. Special categories called topoi can even serve as an alternative to set theory as the foundation of mathematics. Category theory is half-jokingly known as "abstract nonsense". A category attempts to capture the essence of a class of related mathematical objects, for instance the class of groups . Instead of focusing on the individual objects (groups) as has been done traditionally, the

23. Limit (category Theory) - Wikipedia Limit (category theory). In category theory, the limit of a functor generalizes thenotions of inverse limit and product used in various parts of mathematics. http://www.wikipedia.org/wiki/Limit_(category_theory)

Main Page Recent changes Edit this page Older versions Special pages Set my user preferences My watchlist Recently updated pages Upload image files Image list Registered users Site statistics Random article Orphaned articles Orphaned images Popular articles Most wanted articles Short articles Long articles Newly created articles All pages by title Blocked IP addresses Maintenance page External book sources Printable version Talk Log in Help Limit (category theory) From Wikipedia, the free encyclopedia. In category theory , the limit of a functor generalizes the notions of inverse limit and product used in various parts of mathematics . The dual notion, colimit , generalizes direct limits and direct sums . Limits and colimits are defined via universal properties and as such provide many examples of adjoint functors For the formal definition, consider a covariant functor F J C . A limit of F is an object L of C X L F X ) for every object X of J , such that for every morphism f X Y in J , we have F f X Y , and such that the following universal property is satisfied: for any object N of C X N F X ) such that for every morphism f X Y in J , we have F f X Y , there exists precisely one morphism u N L X X for all X If F has a limit (which it need not), then the limit is defined up to a unique isomorphism, and is denoted by lim

24. School On Category Theory And Applications University of Coimbra, Portugal; 1317 July 1999.Category Science Math Algebra category theory Events Past Events......SCHOOL ON category theory AND APPLICATIONS. This school is being organizedby the category theory Group of the University of Coimbra. http://www.mat.uc.pt/~scta/

SCHOOL ON CATEGORY THEORY AND APPLICATIONS Department of Mathematics University of Coimbra PORTUGAL July 13-17, 1999 Welcome to the web site of the School on Category Theory and Applications, which will take place from Tuesday morning, 13 July 1999, through Saturday morning, 17 July, in Coimbra, Portugal. This school is being organized by the Category Theory Group of the University of Coimbra. Programme Timetable New! Organizing Committee Location Support Registration ... Universidade de Coimbra Apartado 3008 3000 Coimbra PORTUGAL Phone: +351-39-791150 Fax: +351-39-832568 E-mail: scta@mat.uc.pt Last updated: June 9, 1999 by Jorge Picado

25. CT99 Category Science Math Algebra category theory Events Past Events http://www.mat.uc.pt/~ct99/

26. Ccard V2.0 - A Category Theory Card Game The official site for this abstract mathematical card game. You can download the deck as a gzipped Category Games Card Games Special Decks Ccard...... What is category theory? In a way, this game is still work in progress(as learning category theory is rather a journey than a goal). http://www.verify-it.de/sub/ccard/

This page is part of the Mozilla Open Directory project Ccard 2.0 or: How to make fun out of something highly abstract. Ccard is a card game. You can download the cards as gzipped postscript here (to be printed 2-sided) or here (single sided) with extra backside It was born in an area of distress in May 1999, kicked of by the Summer School in Semantics (at BRICS, Aarhus University, Denmark) and in particular the course about category theory there. How to play? There are some simple "rules" I made up for two or more players (but you are of course free to change them). The seven suits are organized by a increasing number of "circles" which are meant to reflect the "difficulty" of the facts within. The number of circles/triangles of the suite symbol determines the rank of this suite. Every suite has nine cards. The highest card of one suit is the "aleph"_lambda (resembles a shaky N), followed by "omega", "infinity", then 11, 7, 5, 3, 2 (I like to stick with prime numbers) and finally the empty set (or "naught"). Each of 2 (or possibly more) players gets six cards, the rest is left as a pile on the table.

27. Basic Category Theory Basic category theory. Jaap van Oosten. It is, in the author's view, the very minimumof category theory one needs to know if one is going to use it sensibly. http://www.brics.aau.dk/BRICS/LS/95/1/BRICS-LS-95-1/BRICS-LS-95-1.html

Basic Category Theory Jaap van Oosten January 1995 Abstract: This course was given to advanced undergraduate and beginning Ph.D. students in the fall of 1994 in Aarhus, as part of Glynn Winskel's semantics course. It is, in the author's view, the very minimum of category theory one needs to know if one is going to use it sensibly. Nevertheless, two topics are breathed on, which may be skipped: there is a glimpse of categorical logic, and there is a treatment of the -calculus in cartesian closed categories. These are there to give the reader at least a very rough idea of how the theory ``works''. The text contains a bit over hundred exercises, varying in difficulty, which supplement the treatment and are warmly recommended. There is an elaborate index. Contents Categories and Functors Definitions and examples Some special objects and arrows Natural transformations The Yoneda lemma Examples of natural transformations Equivalence of categories; an example (Co)cones and (co)limits Limits Limits by products and equalizers Colimits A little piece of categorical logic Regular categories and subobjects Coherent logic in regular categories The language and theory associated to a regular category Example of a regular category Adjunctions Adjoint functors Expressing (co)completeness by existence of adjoints; preservation of (co)limits by adjoint functors

28. CoACT.html CENTRE OF AUSTRALIAN category theory (CoACT). A major project of the Centre isthe application of higher dimensional category theory to computer science. http://www.maths.mq.edu.au/~street/CoACT.html

Use these links for further information the CoACT logo titles and abstracts of talks in the Australian Category Seminar; CoACT Managerial Statements (Vision, Mission, Justification, Objectives, Performance Indicators, Benchmarks, and Constitution); Current members and recent visitors; Scott Russell Johnson Memorial Scholarships Macquarie University Calendar entry. CENTRE OF AUSTRALIAN CATEGORY THEORY (CoACT) A Macquarie University Research Centre PROFILE Director: Professor Ross Street PhD, FAustMS, FAA Professor of Mathematics Mathematics Department , Macquarie University Associate Director: Professor Michael Johnson PhD Director of the Macquarie ICT Innovations Centre Division of ICS , Macquarie University External Advisory Board Members: Professor G. Max Kelly PhD, FAA Professorial Fellow and Emeritus Professor School of Mathematics and Statistics , University of Sydney Dr Wesley Phoa BSc ANU, PhD Cambridge Capital Strategy Research The Capital Group Companies , Los Angeles Honorary Consultant Associate Professor Dominic Verity PhD Cambridge Postgraduate Coursework Programs Director Division of ICS , Macquarie University (Previously Director of Categorical Solutions General Description of the Area: Categories concern transformation and composition in mathematics. They provide an algebra of wide-spread applicability for the synthesis and analysis of systems and processes in fields as diverse as physics and computer science, but also in mathematics itself. They can be used to clarify and simplify the learning, teaching and development of mathematics. The aim of the Centre is basic research on categories, training of high quality mathematics and computer science students, and application to geometry, physics, computing, finance, and other industries.

29. Category Theory -- From MathWorld Eric's other sites. Foundations of Mathematics , category theory v. CategoryTheory, The objects studied in category theory are called categories. Category. http://mathworld.wolfram.com/CategoryTheory.html

Foundations of Mathematics Category Theory Category Theory The branch of mathematics which formalizes a number of algebraic properties of collections of transformations between mathematical objects (such as binary relations, groups, sets, topological spaces, etc.) of the same type, subject to the constraint that the collections contain the identity mapping and are closed with respect to compositions of mappings. The objects studied in category theory are called categories Category Author: Eric W. Weisstein Wolfram Research, Inc.

30. Category Theory Authors/titles Recent Submissions category theory. Authors and titles for recent submissions. http://arxiv.org/list/math.CT/recent

Category Theory Authors and titles for recent submissions Tue, 18 Mar 2003 Mon, 17 Mar 2003 Mon, 10 Mar 2003 Thu, 6 Mar 2003 ... Wed, 5 Mar 2003 Tue, 18 Mar 2003 math.FA/0303186 abs ps pdf other Title: Very badly approximable matrix functions Authors: V.V. Peller S.R. Treil Comments: 27 pages Subj-class: Functional Analysis; Classical Analysis and ODEs; Combinatorics; Category Theory; Complex Variables MSC-class: Mon, 17 Mar 2003 math.CT/0303175 abs pdf Title: Categorical and combinatorial aspects of descent theory Authors: Ross Street Comments: 45 pages Subj-class: Category Theory; K-Theory and Homology MSC-class: Mon, 10 Mar 2003 math.CT/0303083 abs ps pdf other Title: Paracategories I: internal parategories and saturated partial algebras Authors: Claudio Hermida Paulo Mateus Subj-class: Category Theory MSC-class: Thu, 6 Mar 2003 math.KT/0303050 abs ps pdf other Title: N-Fold Cech Derived Functors and Generalised Hopf type formulas Authors: Guram Donadze Nick Inassaridze Timothy Porter Comments: LaTex, 30 pages, uses xypic Subj-class: K-Theory and Homology; Category Theory

31. Category Theory Authors/titles Dec 2002 category theory. Authors and titles for Dec 2002. Higgins Comments3 pages. Latex2E Subjclass Algebraic Topology; category theory http://arxiv.org/list/math.CT/0212

Category Theory Authors and titles for Dec 2002 math.CT/0212065 abs ps pdf other Title: Group Objects and Internal Categories Authors: Magnus Forrester-Barker Comments: 12 pages, expository article Subj-class: Category Theory math.OA/0212136 abs ps pdf other Title: Notes on Operator Categories Authors: Shigeru Yamagami Comments: 13 pages Subj-class: Operator Algebras; Category Theory MSC-class: math.AT/0212157 abs ps pdf other Title: Cubical abelian groups with connections are equivalent to chain complexes Authors: R. Brown Philip J. Higgins Comments: 3 pages. Latex2E Subj-class: Algebraic Topology; Category Theory math.CT/0212197 abs ps pdf other Title: A remark on a theorem by Deligne Authors: M. Van den Bergh Comments: 2 pages Subj-class: Category Theory; Algebraic Geometry MSC-class: math.CT/0212219 abs ps pdf other Title: Remarks on 2-Groups Author: Aaron D. Lauda Comments: 32 pages LaTeX with XY-pic figures Subj-class: Category Theory math.AG/0212237 abs ps pdf other Title: Stability conditions on triangulated categories Authors: Tom Bridgeland Comments: 21 pages Subj-class: Algebraic Geometry; Category Theory

32. Part III Category Theory Part III category theory. This is the main page for the Part III CategoryTheory course given in Cambridge in the academic year 20002001. http://www.dpmms.cam.ac.uk/~leinster/categories/

Part III Category Theory Michaelmas/Autumn/Fall 2000, 24 lectures This is the main page for the Part III Category Theory course given in Cambridge in the academic year 2000-2001. All the documents produced for the course were placed here, and all of them apart from the synopsis are in the PostScript (.ps) format. Here is the lecture synopsis and recommended reading list. Here is an informal introduction to Category Theory (10 pages). The first two-thirds of this is a set of notes from the very first lecture. What's the Yoneda Lemma all about? (9 pages) A few more applications of the General Adjoint Functor Theorem , to add to the one given in lectures (one page). Section E2: The Special Adjoint Functor Theorem (7 pages, examinable!). Section F4: The Monadicity Theorem (10 pages, also examinable). Problem sheets: Sheet 1 Sheet 2 Sheet 3 (limits) Sheet 4 Here is a sheet telling you roughly what background mathematical knowledge I'm going to assume you have when I'm setting the exam. Here is a list of known mistakes in the lecture notes and problem sheets, last updated 9 December 2000. Please

33. Category Theory Seminar Mich 02 DPMMS Research category theory Seminar Mich 02. category theory Seminarsfor Michaelmas Term 2002. Archive of category theory Seminars http://www.dpmms.cam.ac.uk/Seminars/Category/

Department of Pure Mathematics and Mathematical Statistics DPMMS Research Category Theory Seminars for Michaelmas Term 2002 Archive of Category Theory Seminars Meetings are held at 2.15pm on Tuesdays in Room MR9 of the CMS. Here is the timetable for this term's seminars. Note that there will be one seminar on a Thursday (6th March). For further information contact Eugenia Cheng Tuesday January 28 Nicola Gambino Heyting-valued interpretations for Constructive Set Theory Tuesday February 4 Marcelo Fiore Category objects as complex numbers Tuesday February 11 Martin Hyland Embedded theorems for closed multicategories Tuesday February 18 Toby Kenney TBA Tuesday February 25 Peter Johnstone The topos of music Thursday March 6 John Power A universal embedding for the higher order structure of computational effects Tuesday March 11 Eugenia Cheng Pseudo-distributive laws Last modified: 10:56 Fri Oct 25 2002 Information provided by webmaster@dpmms.cam.ac.uk

34. CT2000 Villa Olmo, Como, Italy; 1622 July 2000.Category Science Math Algebra category theory Events Past Events......CT2000. International category theory Conference. Villa Olmo, Como, July 1622, 2000.If you see this, it probably means that your browser does not handle frames. http://www.disi.unige.it/conferences/ct2000/

International Category Theory Conference Villa Olmo, Como, July 16-22, 2000 If you see this, it probably means that your browser does not handle frames. Follow the link to Detailed Information or that to the map of the site . Clicking buttons from there on may open pages in new windows, else remember to use your Back button to return to that page.

35. Category Theory And Aldor category theory in Aldor. The idea is to begin a library of Aldor categoriesand domains organized around category theory in the mathematical sense. http://physics.bu.edu/~youssef/aldor/aldor.html

Aldor Related Projects Category Theory in Aldor The idea is to begin a library of Aldor categories and domains organized around category theory in the mathematical sense. In more detail, the goals are to a) find working design patterns for categories, functors, natural transformations, adjoints within Aldor b) encode known facts about category theory (the adjoint functor theorem, for example) into the system c) produce a library implementing the most basic and useful categories. Here's a recent talk and the draft of a paper Prospects for Category Theory in Aldor Computing with Category Theory Saul Youssef

36. The Math Forum - Math Library - Cat. Theory/Homolgcl Alg. sites and Web pages relating to the study of mathematics. This pagecontains sites relating to category theory/Homological Algebra. http://mathforum.org/library/topics/category_theory/

Browse and Search the Library Home Math Topics Algebra Modern Algebra : Cat. Theory/Homolgcl Alg. Library Home Search Full Table of Contents Suggest a Link ... Library Help Selected Sites (see also All Sites in this category Category Theory, Homological Algebra - Dave Rusin; The Mathematical Atlas A short article designed to provide an introduction to category theory, a comparatively new field of mathematics that provides a universal framework for discussing fields of algebra and geometry. While the general theory and certain types of categories have attracted considerable interest, the area of homological algebra has proved most fruitful in areas of ring theory, group theory, and algebraic topology. History; applications and related fields and subfields; textbooks, reference works, and tutorials; software and tables; other web sites with this focus. more>> All Sites - 19 items found, showing 1 to 19 Applied and Computational Category Theory - RISC-Linz, Austria A brief history and description of category theory, and some related links. From the Research Institute for Symbolic Computation. ...more>> Categories, Quantization, and Much More - John Baez

37. About "Applied And Computational Category Theory At RISC-Linz" Applied and Computational category theory at RISCLinz. Library Home Full Table of Contents Suggest a Link Library Help http://mathforum.org/library/view/12862.html

Applied and Computational Category Theory at RISC-Linz Library Home Full Table of Contents Suggest a Link Library Help Visit this site: http://www.risc.uni-linz.ac.at/research/category/risc/ Author: Description: Researchers; research topics; publications; events; e-mails from the Category Theory mailing list maintained and moderated by Bob Roseburgh, sorted by subject; positions announcements disseminated through the Category Theory mailing list; relevant links. For a general history and description of the research area, see Applied and Computational Category Theory. Levels: Research Languages: English Resource Types: Research Centers Math Topics: Algebraic Topology Suggestion Box Home The Math Library ... Search http://mathforum.org/ webmaster@mathforum.org

38. Category Theory Reference category theory Reference. MetaCat. The metacategory of all categories.Image map; Postscript. (Generated by dot .). Index. Abcategory; http://www.maths.qmul.ac.uk/~mh/categories/

Category Theory Reference MetaCat The metacategory of all categories. Image map Postscript (Generated by dot Index Ab-category Abelian groups Abelian semigroups Bimodules ... topos category These reference pages were auto-generated from XML files on Wed Jul 31 14:55:11 GMT 2002.

39. Graphical Database For Category Theory Introduction; Download; Documentation; Bug Report; Contact Us. GDCTVersion 1.1 Webpage Page Modified by Matthew Graves June 27, 2002. http://mathcs.mta.ca/research/rosebrugh/gdct/

Introduction Download Documentation Bug Report ... GDCT Version 1.1 Webpage Page Modified by Matthew Graves June 27, 2002

40. Lars Birkedal / Teaching / Category Theory --- Fall 2000 category theory Fall 2000. A number of applications of category theory to computerscience will also be covered, including some recent developments. http://www.itu.dk/~birkedal/teaching/category-theory-Fall-2000/

Category Theory Fall 2000 Instructors: Lars Birkedal birkedal@it-c.dk , Glentevej 67, Room 2.21, 3816 8868 Thomas Hildebrandt hilde@it-c.dk , Glentevej 67, Room 2.46, 3816 8833 Category theory, a branch of abstract algebra, has found many applications in mathematics, logic, and computer science, where it for example has been used to describe and analyse models of both sequential and parallel programming languages. Like such fields as elementary logic and set theory, category theory provides a basic conceptual apparatus and a collection of formal methods useful for addressing certain kinds of commonly occurring formal and informal problems, particularly those involving structural and functional considerations. This course is intended to acquaint students with these methods, and also to encourage them to reflect on the interrelations between category theory and the other basic formal disciplines. A number of applications of category theory to computer science will also be covered, including some recent developments. Course Information Lectures Tuesdays, Glentevej, Room 1.03, 9:00 AM - 12:00 AM, 2:00 PM - 4 PM

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