61. Category Theory: Information From Answers.com category theory category theory is a mathematical theory that deals in an abstractway with mathematical structures and relationships between them. http://www.answers.com/topic/category-theory

showHide_TellMeAbout2('false'); Business Entertainment Games Health ... More... On this page: Wikipedia Best of Web Mentioned In Or search: - The Web - Images - News - Blogs - Shopping category theory Wikipedia category theory Category theory is a mathematical theory that deals in an abstract way with mathematical structures and relationships between them. It is half-jokingly known as "generalized abstract nonsense Categories appear in most branches of mathematics, and in some areas of theoretical computer science and mathematical physics , and have been a unifying notion. Categories were first introduced by Samuel Eilenberg and Saunders Mac Lane in , in connection with algebraic topology See list of category theory topics for a breakdown of relevant articles. Background The study of categories is an attempt to capture what is commonly found in various classes of related mathematical structures. Consider the following example. The class Grp of groups consists of all objects having a "group structure". More precisely, Grp consists of all sets G endowed with a binary operation satisfying a certain set of axioms . One can proceed to prove theorems about groups by making logical deductions from the set of axioms. For example, it is immediately proved from the axioms that the

62. Categories Home Page Web page for the category theory mailing list. http://www.mta.ca/~cat-dist/

Categories List How to use the list Archives Moderator Conferences of interest ... Addresses - electronic and postal General, Seminar-related, and Local Sites Theory and Applications of Categories - refereed electronic journal. TeX Macros for diagrams Using the list: Articles for posting should be sent to categories@mta.ca Administrative items (subscriptions, address changes etc.) should be sent to categories-request@mta.ca Usually, items of this sort sent to `categories@mta.ca' will not be posted. Policy: The moderator will not modify articles except for minor typographical and formatting changes, therefore no offensive or defamatory material should be sent (it will be returned and not posted), and inflammatory posts are discouraged. Nevertheless, wide latitude for vigorous debate is allowed. Return to top. Archives M. Alsani has created a selected list of CT email, also sorted by thread, from August 1999 to February 2002 at http://north.ecc.edu/alsani/cat-dist2html/index.html A subject-sorted list of postings June 1994-December 1999 is at www.mta.ca/~cat-dist/catlist/

63. CTCS97 7th conference on category theory and Computer Science. S. Margherita Ligure, Italy; 46 September 1997. http://www.disi.unige.it/conferences/ctcs97/

CTCS'97, 4-6 September 1997, S. Margherita Ligure, Italy URL "http://www.disi.unige.it/conferences/ctcs97/" CTCS'99 (Edinburgh) Conference Programme and Abstracts of accepted papers Travel Information List of Participants CTCS'97 is the 7th conference on Category Theory and Computer Science . The purpose of the conference series is the advancement of the foundations of computing using the tools of category theory, algebra, geometry and logic. While the emphasis is upon applications of category theory, it is recognized that the area is highly interdisciplinary. The proceedings will be published by Springer as volume 1290 in the LNCS series. The conference will take place at Hotel Regina Elena , a 4 stars hotel with private beach, located in S. Margherita Ligure . This is a beautiful sea resort in Liguria very close to Portofino promontory and about 30 km east of Genova Programme committee S. Abramsky Edinburgh (UK) P.-L. Curien LIENS (France) P. Dybjer Chalmers (Sweden) P. Johnstone Cambridge (UK) G. Longo

64. Category Theory And Homotopy Theory category theory was introduced in 1947 to give a richer language than that of set The basic areas of research in category theory at Bangor are directed http://www.informatics.bangor.ac.uk/public/research/mathematics/cathom/cathom1.s

Personnel Collaborators Prof Tim Porter Prof Ronnie Brown Mr Alinor Abdul Kadir Mr Magnus Forrester-Barker Prof Heiner Kamps Prof George Janelidze (Georgia) Dr Manuela Sobral (Coimbra) Dr Manuel Bullejos Prof Tony Bak (Bielefeld) Dr Gabriel Minian (Max Planck, Bonn) Introduction Category theory was introduced in 1947 to give a richer language than that of set theory, which would be better able to express the structures of homotopy and homology theory then being revealed in the work of Cartan, Eilenberg, Mac Lane, Whitehead and others. In addition to the objects in a category (corresponding to the elements in a set), one also has arrows or "morphisms" between them. Thus for instance the collection of all sets and functions between them forms a category, the category of sets. This language and theory was soon found to have great usefulness in other branches of pure mathematics such as algebra, algebraic geometry, logic and more recently in computer science. The basic areas of research in category theory at Bangor are directed towards achieving a greater understanding of the categorical structure and interrelationships between the various objects studied by algebraic topology and homological algebra. Recent work in these areas has resulted in a large group of fascinating new structures. These have not yet revealed all their categorical structure nor have all the potential applications of these objects been fully investigated.

65. Paul Taylor Includes papers on category theory. http://www.cs.man.ac.uk/~pt/

Paul Taylor Senior Research Fellow (RA3) funded by EPSRC GR/S58522 Abstract Stone Duality Please contact me by electronic mail: pt @ cs.man.ac.uk Please note that I am physically in London, not Manchester . If you want to send me something by post, telephone me or visit me, please email me first or see the directions to my house My current research programme is called Abstract Stone Duality ; three papers about it have been published in Theory and Applications of Categories My book, Practical Foundations of Mathematics , was published by Cambridge University Press in 1999, ISBN 0-521-63107-6. I am also interested in induction, recursion, replacement and the ordinals from a categorical point of view. My PhD thesis and early post-doctoral work was on (classical, continuous, Scott-style) domain theory , after which I studied stable domain theory The first year computer science course that I taught when I was a lecturer at Queen Mary, University of London

66. ATCAT Dalhousie University, Halifax. Weekly meetings. 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@mathstat.dal.ca 2005-2006 Participants List of talks The Naming of Cats - T.S.Eliot

67. Category Theory - Definition Of Category Theory In Encyclopedia category theory is a mathematical theory that deals in an abstract way withmathematical structures and relationships between them. http://encyclopedia.laborlawtalk.com/Category_theory

Add to Favorites General Encyclopedia Legal ... Law forum Search Word: Visit our Law forums Labor Law Accidents Law Bankruptcy Law Business Law ... Tax Law Category theory is a mathematical theory that deals in an abstract way with mathematical structures and relationships between them. It is half-jokingly known as "generalized abstract nonsense See list of category theory topics for a breakdown of relevant articles. Contents showTocToggle("show","hide") 1 Background 2 Historical notes 3 Categories 3.1 Definition ... 12 External links Background 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 morphisms —i.e. the structure-preserving maps between these objects—are emphasized. In the example of groups, these are the group homomorphisms . Then it becomes possible to relate different categories by functors , generalizations of functions which associate to every object of one category an object of another category and to every morphism in the first category a morphism in the second. Very commonly, certain "natural constructions", such as the fundamental group of a topological space , can be expressed as functors. Furthermore, different such constructions are often "naturally related" which leads to the concept of

68. CRTC -- Montréal -- Seminars Timetable. http://www.math.mcgill.ca/rags/seminar/

Category Theory Research Center Seminars scheduled in 2005-2006 20 Sept 2004 2:30 - 4:00 Gadi Moran From Monotone Functions to Scattered Orders (Abstract) PLACE: BURNSIDE HALL 920, McGILL UNIVERSITY (COOKIES AND COFFEE AFTER THE TALK, IN THE LOUNGE) If you wish to receive regular updates to this list by email, send your request to be added to the e-list to RAG Seely (rags@math.mcgill.ca) (Other seminars in Montreal) Seminars and abstracts from 1998-1999 Seminars and abstracts from 1999-2000 Seminars and abstracts from 2000-2001 Seminars and abstracts from 2001-2002 ... Octoberfest 99 Seminars from previous years (rough listings) Octoberfest '95 Barrfest '97

69. The Math Forum - Math Library - Cat. Theory/Homolgcl Alg. catalog of Web sites and Web pages relating to the study of mathematics.This page contains 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

70. Category Theory category theory looks at mathematics on a large scale objects and the relationsbetween them, in the abstract. The aim is to strip away inessential details http://www.maths.gla.ac.uk/research/groups/categoryth/

Text only Department of Mathematics Home Research > Category Theory Home Research Algebra Analysis ... Contact Category Theory Category theory looks at mathematics on a large scale: objects and the relations between them, in the abstract. The aim is to strip away inessential details and get to the essence of things. By doing this one finds fundamental concepts - "category" and "functor" being well-known examples - that are very general and therefore invite comparisons between apparently unrelated parts of mathematics. Put another way, if you screw up your eyes then you can sometimes see the similarity between objects that you had previously thought quite different. Much of modern mathematics is, literally, near-unthinkable without the organizing principles of category theory. This is especially true of algebraic geometry, topology, homological algebra, logic, and theoretical computer science, and increasingly many parts of the mathematical sciences (physics, particularly) are finding categorical ways of thinking to be useful. Dr Tom Leinster works mainly on higher-dimensional algebra. Naively, this is algebra that cannot be expressed naturally by writing along one-dimensional lines in the customary way; practically, it is the study of structures such as n-categories, operads, and multicategories. These structures are officially algebraic, but have a very high geometric content: naively again, it is almost impossible to understand them without drawing some pictures; at a more sophisticated level, there appear to be intimate connections between higher categorical structures and both homotopy theory and topological quantum field theory. An informal survey of such connections is "

71. CTCS'02 category theory and Computer Science. University of Ottawa, Ontario, Canada; 1517 August 2002. http://www.mathstat.uottawa.ca/lfc/ctcs2002/

Category Theory and Computer Science (CTCS'02) August 15th-17th, 2002 University of Ottawa and Graduate Student Preconference August 12-14, 2002 Pictures from the conference. Thanks to all participants for a successful conference! Several people have taken pictures at the conference, and I will link to them from this page. Pictures by Masahito Hasegawa Pictures by Anjayan Puvananathan The purpose of this conference series is the advancement of the foundations of computing, using the tools of category theory. While the emphasis is on applications of category theory, it is recognized that the area is highly interdisciplinary. Category theory, after having played a major role in the development of mathematics, e.g. in algebraic geometry, has been widely applied by logicians to obtain concise interpretations of many logical concepts. On the other hand, links between logic and computer science have been developped now for over twenty years, notably via the Curry-Howard isomorphism, which identifies programs with proofs. Together, the triangle category theory-logic-computation presents a rich world of interconnections. It is the primary purpose of the CTCS conference series to explore these interconnections. In addition to the usual three day conference, there will be a three day "preconference", which is designed to prepare students, both graduate and undergraduate, to participate in the conference. The preconference will take place from August 12-14.

72. (Canada) University Of Calgary Calgary Peripatetic Research Group in Logic and category theory alternates between departments of mathematics, philocophy, and computer science; meets weekly. http://pages.cpsc.ucalgary.ca/~luigis/CPRGLCC/

Calgary Peripatetic Research Group on Logic and Category Theory Meetings on Logic and Category Theory to be held in the Philosophy Mathematics and Computer Science Departments of the University of Calgary TIME: Monday 2:10pm (weekly) , PLACE: ICT 616 (or as arranged). Fall 2001: next seminar, incoming seminars, past seminars. Participants For talk titles, abstracts, comments etc. contact Luigi Santocanale

73. LtU Classic Archives Andris Birkmanis Re Elements of Basic category theory blueArrow I like tothink about category theory as emphasizing specifications or outer http://lambda-the-ultimate.org/classic/message11222.html

Lambda the Ultimate Elements of Basic Category Theory started 2/16/2004; 5:07:07 AM - last post 2/21/2004; 5:04:09 AM Ehud Lamm - Elements of Basic Category Theory 2/16/2004; 5:07:07 AM (reads: 9096, responses: 24) Elements of Basic Category Theory Andris gave this link in the discussion group. I took a quick look and it looks quite nice. Posted to theory by Ehud Lamm on 2/16/04; 5:08:34 AM Andris Birkmanis - Re: Elements of Basic Category Theory 2/16/2004; 11:03:48 AM (reads: 846, responses: 1) I liked the ability to define a diagram categorically, providing a visual intuition for functors at the same time (6.1.5). Before this book, I saw only "visual" metaphor of natural transformations being "slides" from one functor to another (which was not very helpful without being able to easily visualize functor). Now it's a snap. [on edit - not that I never saw diagrams, but it never occurred to me that each diagram with a categorical scheme is a visualization of a functor - and vice versa] One just needs to be aware that each author has slightly different definitions, e.g., many authors do not require schemes of diagrams to be categories themselves (just general graphs). This, of course, does not serve well to the theory in general, and undermines its use as a common dictionary for discussion of problems. The worst, probably, is unability to use intuition developed for definitions of one author working with text written by another :-( On the bright side, (I think) there are not many such divergence points in category theory. Can you share your experience?

74. CompCat At Bangor Computational category theory (part of The Computational category theory Project). People, activities, software. http://www.informatics.bangor.ac.uk/public/math/research/compcat/

University of Wales, Bangor - School of Informatics Computational Category Theory This site is part of The Computational Category Theory Project. Groups Currently connected with this project are: Contact: Bob Walters at: robert.walters@uninsubria.it Mount Allison University, Canada Contact: Bob Rosebrugh at: RRosebrugh@mta.ca This group Contact: Ronnie Brown at: R.Brown@bangor.ac.uk Goals and Method The aim of this project is the development of software on a wide variety of platforms for computing with mathematical categories and associated algebraic structures. Although writing on different platforms each group will undertake to make available programs for translating their input and output files to the formats of the other groups. New versions will be announced on the Categories Mailing List. Background to Activities at Bangor Participants Background Papers Software developed at Bangor XMOD - (Wensley/Alp) GAP3 package for crossed modules and cat1-groups (currently being converted to GAP4.1); KAN - (Heyworth) GAP3 package for Kan extensions of actions of categories (currently being converted to GAP4.1).

75. Elementary Category Theory | Lambda The Ultimate That s how you say A is a subset of B in category theory. For those interestedin a brief introduction to category theory, James Cheney has recently http://lambda-the-ultimate.org/node/view/39

@import url(misc/drupal.css); Lambda the Ultimate Home Feedback FAQ ... Archives User login Username: Password: Create new account Request new password Navigation recent posts Home Forums LtU Forum Elementary Category Theory Recently I started learning CT, and I'm trying to express the property "set A is contained within set B" (in the Set Category) using CT language only, but I'm quite stuck. This bothers me for some time now, so I was wondering if someone here has any leads? Thanks in advance! By Ohad Kammar LtU Forum login or register previous forum topic next forum topic other blogs Comment viewing options Flat list - collapsed Flat list - expanded Threaded list - collapsed Threaded list - expanded Date - newest first Date - oldest first 10 comments per page 30 comments per page 50 comments per page 70 comments per page 90 comments per page 150 comments per page 200 comments per page Select your preferred way to display the comments and click 'Save settings' to activate your changes. CT Subset Have you tried "there is a monomorphism from A to B" as a starting point? If you are interested in a CT version of Set Theory, try "Conceptual Mathematics" by Lawvere and Schanuel or "Sets for Mathematics" by Lawvere and Rosebrugh.

76. Number Theory category theory begins with the observation (EilenbergMac Lane 1942) that the category theory has had great success in the unification of ideas from http://www.maths.cam.ac.uk/CASM/courses/descriptions/node34.html

Next: Cyclotomic Fields (L24) Up: Mathematical Tripos Part III Previous: Set Theory (L24) Number Theory Subsections Cyclotomic Fields (L24) Topics in Number Theory (M16) Analytic Number Theory (L16) Elliptic Curves (L24)

77. Computational Category Theory At Macquarie Computational category theory project group. People, projects, publications. http://www.ics.mq.edu.au/~mike/compcat/

Computational category theory projects at Macquarie Participants Michael Johnson Kit Dampney Kate Krastev Dominic Verity ... Robbie Gates Projects Case support for category theoretic specification of information systems Case support for modelling concurrency with n-categorical pasting schemes The theory of generalised distributivities Computational algebra and monoid theory (joint with Anne Heyworth, Leicester) Publications Until this page is better developed you can get some idea of some of the work we do by looking at the following publications, most (but not all) of which relate to computational category theory and what we seek to do with the tools these projects are developing. Recent Publications (updated September 2000) Selected Older Publications The International Computational Category Theory Project This site is part of The Computational Category Theory Project Groups Currently connected with this project are: Como, Italy Contact: R.F.C. Walters Walters@fis.unico.it University of North Wales, Bangor, Wales Contact: R. Brown

78. Bookpool: Basic Category Theory For Computer Scientists category theory is a branch of pure mathematics that is becoming an Assuming aminimum of mathematical preparation, Basic category theory for Computer http://www.bookpool.com/sm/0262660717

help account NEW RELEASES BEST SELLERS ... LOG IN Basic Category Theory for Computer Scientists View Larger Image Benjamin C. Pierce MIT Press, Paperback, Published September 1991, 100 pages, ISBN 0262660717 List Price: $25.00 Our Price: You Save: $5.50 (22% Off) Availability: In-Stock Be the First to Write a Review and tell the world about this title! People who purchase this book frequently purchase: Haskell School of Expression, The: Learning Functional Programming Through Multimedia Paul Hudak 27% Off! Books on similar topics, in best-seller order: Hardware Books from the same publisher, in best-seller order: MIT Press Category theory is a branch of pure mathematics that is becoming an increasingly important tool in theoretical computer science, especially in programming language semantics, domain theory, and concurrency, where it is already a standard language of discourse. Assuming a minimum of mathematical preparation, Basic Category Theory for Computer Scientists provides a straightforward presentation of the basic constructions and terminology of category theory, including limits, functors, natural transformations, adjoints, and cartesian closed categories. Four case studies illustrate applications of category theory to programming language design, semantics, and the solution of recursive domain equations. A brief literature survey offers suggestions for further study in more advanced texts. Benjamin C. Pierce received his doctoral degree from Carnegie Mellon University. About the Author

79. Computational Category Theory At Mt Allison Computational category theory. Software, people. http://www.mta.ca/~rrosebru/compcat/compcat.html

The Computational Category Theory Project at Mount Allison University This site is part of The Computational Category Theory Project. Goals and Method. The aim of this project is the development of software on a wide variety of platforms for computing with mathematical categories and associated algebraic structures. Although writing on different platforms each group will undertake to make available programs for translating their input and output files to the formats of the other groups. Software developed at Mount Allison Graphical Database for Category Theory Java application - Version 1.0 (January 2000) mathcs.mta.ca/research/rosebrugh/gdct/ Developed in 1998, a Java applet: Category Theory Database Tools by J. Bradbury and R. Rosebrugh. Warning: The applet is a 700Kb download. Improved version coming 99/9. Completed in 1995, a menu-based C program: A Database of Categories Other Members Ronnie Brown School of Mathematics, University of Wales, Bangor, Wales Anne Heyworth MCS, University of Leicester, England ... Bob Rosebrugh

80. Basic Category Theory Basic category theory. Jaap van Oosten. January 1995 It is, in the author sview, the very minimum of category theory one needs to know if one is going http://www.brics.dk/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

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