41. Category Theory. [Archive] - Physics Forums 19 posts 9 authors - Last post Feb 17There s alway wikipedia (http//en.wikipedia.org/wiki/category_theory). Dummitt and Foote has a decent intro to category theory as an http://www.physicsforums.com/archive/index.php/t-156093.html

Physics Forums Mathematics Set Theory, Logic, Probability, Statistics PDA View Full Version : Category Theory. Son Goku Feb13-07, 11:44 AM Essentially I'd just like to learn more about it in my own spare time. Is there any particularly good introductory books or articles? I'd particularly like anything that uses examples from physics, but it isn't essential. ex-xian Feb13-07, 01:42 PM There's alway wikipedia (http://en.wikipedia.org/wiki/Category_theory). Dummitt and Foote has a decent intro to category theory as an appendix. Dcase Feb13-07, 03:02 PM John Baez is one of the experts in category theory who often posts to his blogs 'n-category Cafe' or 'This Week’s Finds in Mathematical Physics'. Week 245 has talks in this theory from a U-Toronto workshop at the Fields Institute January 9-13, 2007. http://math.ucr.edu/home/baez/week245.html matt grime Feb13-07, 05:41 PM John Baez is not an expert in category theory. Mac Lane is the standard book, but it is very hard going. mathwonk Feb13-07, 09:21 PM i liked peter freyd's little book in the 60's and 70's. hungerford ahs a short little section that helps too.

42. Category Theory - Slider Category theory is a mathematical theory that deals in an abstract way with mathematical structures and relationships between them. Categories appear in most branches of http://enc.slider.com/Enc/Category_theory

Advanced Help Encyclopedia Directory Encyclopaedia C Ca Caa ... Caz Category theory Category theory is a mathematical theory that deals in an abstract way with mathematical structures and relationships between them. 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 Category theory is half-jokingly known as "generalized abstract nonsense ". See list of category theory topics for a breakdown of relevant articles. Table of contents Background Historical notes Categories Definition ... Notes 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

43. Basic Category Theory 1 Definition And Examples File Format PDF/Adobe Acrobat Quick View http://www.mast.queensu.ca/~cesar/math_notes/category_theory.pdf

44. Category Theory - CUNY GC MathWiki Dec 19, 2006 Category theory is, roughly speaking, the study of abstract structure. That is, a category theoretic view of a particular situation makes http://mathwiki.gc.cuny.edu/index.php/Category_Theory

Category Theory From CUNY GC MathWiki Jump to: navigation search Category theory is, roughly speaking, the study of abstract structure. That is, a category theoretic view of a particular situation makes the underlying structure explicit, and illustrates precisely where content 'colors' this abstract structure. Topics in Category Theory Category Functor Functorial Factorization Natural Transformation ... Product as Kan Extension Retrieved from " http://mathwiki.gc.cuny.edu/index.php/Category_Theory Views Page Discussion View source History Personal tools Log in Navigation Main Page Current events Courses Lectures ... Help Search Toolbox What links here Related changes Special pages Printable version ... Permanent link This page was last modified on 19 December 2006, at 17:52. This page has been accessed 339 times. About CUNY GC MathWiki

45. Contribution ConCaT The Coq Proof Assistant category_theory.NT.HomFunctor_NT ConCaT.category_theory.ADJUNCTION.CCC.CCC1 ConCaT.category_theory.LIMITS.CoUniversalArrow ConCaT.SETOID. http://www.lix.polytechnique.fr/coq/contribs/ConCaT.html

46. Category Theory (Stanford Encyclopedia Of Philosophy) This expository article is an entry in the Stanford Encyclopedia of Philosophy. http://plato.stanford.edu/entries/category-theory/

Cite this entry Search the SEP Advanced Search Tools ... Please Read How You Can Help Keep the Encyclopedia Free Category Theory First published Fri Dec 6, 1996; substantive revision Thu Feb 25, 2010 1. General Definitions, Examples and Applications 2. Brief Historical Sketch 3. Philosophical Significance Bibliography ... Related Entries 1. General Definitions, Examples and Applications 1.1 Definitions et al . 2000, 2001, 2002). The very definition of a category is not without philosophical importance, since one of the objections to category theory as a foundational framework is the claim that since categories are defined Definition : A mapping e will be called an identity if and only if the existence of any product e e implies that e e Definition C is an aggregate Ob of abstract elements, called the objects of C , and abstract elements Map , called mappings of the category. The mappings are subject to the following five axioms: is defined. When either is defined, the associative law are defined. e e is defined, and at least one identity e such that e (C4) The mapping e X corresponding to each object X is an identity.

47. Centre De Recherche En Théorie Des Catégories -- Montréal Category Theory Research Centre. Announcements of weekly seminars, conferences, and other research activities in category theory. http://www.math.mcgill.ca/triples/

Category Theory Research Center Translation? List of current seminars Some upcoming meetings MFPS 26 Twenty-Sixth Conference on the Mathematical Foundations of Programming Semantics, University of Ottawa, Thursday May 6 - Monday May 10, 2010 What is Category Theory? Category Theory at McGill A personal account by Marta Bunge. Category Theory - an expository article from the Stanford Encyclopedia of Philosophy. Theory page. Categorical Logic , an entry by J. Lambek from the Encyclopaedia of Mathematics (Springer). Category , another article from the Encyclopaedia of Mathematics (Springer). Categories, Quantization, and Much More - an introduction by John Baez. (You might also explore his series "This Week's Finds in Mathematical Physics" which often has references to logic , category theory, and particularly n -category theory and more n -category theory . You can also look at these slides: Why and What are n -categories?) Toposes, Triples and Theories A classic text by M Barr and C Wells, now freely available on-line (TACReprints). This is also available at the authors' own website Category Theory for Computing Science (Ordering information for another classic text by M Barr and C Wells, the current version published by the CRM.)

48. 18: Category Theory, Homological Algebra In the known maths series. http://www.math.niu.edu/~rusin/known-math/index/18-XX.html

Search Subject Index MathMap Tour ... Help! ABOUT: Introduction History Related areas Subfields POINTERS: Texts Software Web links Selected topics here 18: Category theory, homological algebra Introduction Category theory, a comparatively new field of mathematics, 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 A survey article which discusses the roles of categories and topoi in twentieth-century mathematics. Applications and related fields The word "category" is used to mean something completely different in general topology Subfields General theory of categories and functors Special categories Categories and algebraic theories Categories with structure Abelian categories Categories and geometry Homological algebra, see also 13DXX, 16EXX, 55UXX This is among the smaller areas in the Math Reviews database. Browse all (old) classifications for this area at the AMS.

49. 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 ... 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 Categories uses Majordomo mailing list software. To receive list email at the address from which you are sending a subscription request, simply write "subscribe" in the body of your message. If you wish to have categories mailings go to a different address, add that address to your message. For instance, you might put the line "subscribe jdoe@my-uni.org" in the mail message body. To terminate your subscription, send the message "unsubscribe". This may fail if your provider has changed the way your address is shown in your mail. To remove an address other than the one from which you are sending the request, give that address in the request: "unsubscribe jdoe@my-uni.org".

50. Introduction To Category Theory Lecture notes by Maarten M. Fokkinga introducing some important notions from category theory, in particular adjunctions. Proofs are given in a calculational style, and the (few http://wwwhome.cs.utwente.nl/~fokkinga/mmf92b.html

A Gentle Introduction to Category Theory - the calculational approach Maarten M Fokkinga In these notes we present the important notions from category theory. The intention is to provide a fairly good skill in manipulating with those concepts formally. What you probably will not acquire from these notes is the ability to recognise the concepts in your daily work when that differs from algorithmics, since we give only a few examples and those are taken from algorithmics. For such an ability you need to work through many, very many examples, in diverse fields of applications. Full paper reachable via: here (80 pages). Bibtex data

51. Categories An implementation of concepts and constructions from category theory in the functional programming language Standard ML. Documentation and code. http://www.cs.man.ac.uk/~david/categories/

Computational Category Theory Welcome to the Computational Category Theory Project Computational Category Theory is an implementation of concepts and constructions from category theory in the functional programming language Standard ML. The original ideas are due to R.M. Burstall, and it was developed by D. Rydeheard, with help from D.T. Sannella and others in the University of Edinburgh theoretical computer science community. The Manual For full details of the project, there is a copy of the manual (in PDF or Postscript) available here The Programs To access the Computational Category Theory programs go to this directory . There is a Readme file giving instructions on compiling and running the programs. Any comments? Please email me at david @ cs.man.ac.uk Contact the Website Administrator with comments or queries about this website.

52. Basic Category Theory For Computer Scientists - The MIT Press Basic Category Theory for Computer Scientists provides a straightforward presentation of the basic constructions and terminology of category theory, including limits http://mitpress.mit.edu/catalog/item/default.asp?ttype=2&tid=7986

53. Category Theory@Everything2.com A branch of mathematics I want to study one day. an extreme form of algebra. In category theory, the primitive notions are nodes and arrows. http://everything2.com/e2node/category%20theory

Near Matches Ignore Exact Everything category theory thing by rp Wed Jul 19 2000 at 13:28:08 A branch of mathematics I want to study one day. an extreme form of algebra In category theory, the primitive notions are nodes and arrows. A category is a set of nodes connected with arrows such that if a path leads from one node to another, so does a direct arrow; in other words, a transitive directed graph Nodes represent sets; arrows represent functions; categories describe particular types of sets entirely in terms of the functions that operate on them, and on related sets. This avoids the overspecification you often get when describing mathematical objects in set theoretic terms. Take a look at the definition of tuple s in terms of set That's as far as I understand it. Remind me to add to this when I finish the textbook. I like it! thing by ariels Fri Sep 01 2000 at 19:58:32 Node s do not really represent set s; this is again the overspecification that we are trying to rebel against. Nodes represent nodes. Arrow s do not represent function s, either.

54. Alsani's Descent & Category Theory WebPage! Maintained by M. Alsani. http://north.ecc.edu/alsani/descent.html

D ESCENT A ND C ATEGORY T HEORY C ONNECTIONS! M. Alsani; alsani@ecc.edu This page is merely a launching pad to sites of interest in Descent or Category Theory. Selected Category Theory E-mail from the Category Theory mailing list Category Theory Archives from the Front for the Mathematics ArXiv site Category Theory Stanford Encyclopedia of Philosophy - Archives CATEGORIES HOME PAGE Bob Rosebrugh Ccard 2.0 - or : How to make fun out of something highly abstract. interactive Web-based demonstrations of concepts in category theory Jocelyn Paine Wikiversity's Introduction to Category Theory Scroll down for lessons. Category (mathematics) From Wikipedia, the free encyclopedia. Category Theory for Beginners Steve Easterbrook TEORIA E APPLICAZIONI DELLE CATEGORIE University of Genoa, Italy Kategorielle Methoden in Algebra und Topologie Texte d'Alexandre Grothendieck (in progress) Categorical Geometry Zhaohua Luo page F. William Lawvere page John Duskin page Toposes, Triples and Theories - A classic text by M Barr and C Wells Descent Theory and its Higher Dimensional Analogues Descent theory and Amitsur cohomology of adjoint functors Slides by Dragos Stefan Geometric and Logical Aspects of Descent Theory Oberwolfach 1995.

55. Redirection To Www.PaulTaylor.EU Includes papers on category theory. http://www.cs.man.ac.uk/~pt/

This page may now be found at www.PaulTaylor.EU to which you should be redirected in 3 seconds. Paul Taylor, 1 August 2007.

56. 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 2009-2010 Participants List of talks The Naming of Cats - T.S.Eliot

57. Category Theory Category Theory General Math discussion Does 'category theory' link different mathematical structures? Can you give a superficial example of how this has been done (eg. http://www.physicsforums.com/showthread.php?t=209552

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

Category Theory Research Center Seminars scheduled in 2010 - 2011 Next talk Thursday 16 September 2010 10:30 - 12:00 M Makkai The first in a series of seminars, Details here Tuesday 21 Sept 2010 2:30 - 4:00 Gadi Moran (Haifa) The discovery of the quaternions - a rediscovery [Abstract] Thursday 30 September 2010 10:30 - 12:00 M Makkai The second in a series of seminars, NOTE: Change of locale: Details here Tuesday 5 October 2010 2:30 - 4:00 J Lambek Visions of six dimensions Abstract: The quaternionic approach to physics and the Lorentz category gain in transparency if one assumes that there are three temporal dimensions. Thursday 14 October 2010 10:30 - 12:00 M Makkai The third in a series of seminars, (room Z-205, Claire McNicoll Building) Details here Thursday 28 October 2010 10:30 - 12:00 M Makkai The fourth in a series of seminars, (room Z-205, Claire McNicoll Building) Details here Thursday 11 November 2010 10:30 - 12:00 M Makkai The next in a series of seminars, (room Z-205, Claire McNicoll Building)

59. Category Theory In NLab Later this will lead naturally on to an infinite sequence of steps first 2category theory which focuses on relation between relations, morphisms between morphisms 2-morphism s http://ncatlab.org/nlab/show/category theory

nLab category theory Skip the Navigation Links Home Page All Pages Recently Revised ... Export Context Mathematics mathematics Structural Foundations logic internal language ... geometry (general list), topology (general list) general topology differential topology differential geometry synthetic differential geometry ... noncommutative geometry (general flavour) higher geometry Algebra universal algebra higher algebra ... Edit this sidebar Category theory category theory Concepts category functor natural transformation Cat Universal constructions universal construction representable functor adjoint functor limit ... Kan extension Theorems Yoneda lemma Isbell duality Grothendieck construction adjoint functor theorem ... Tannaka duality Extensions sheaf and topos theory enriched category theory higher category theory Applications applications of (higher) category theory Edit this sidebar Contents Idea The central constructions Presheaves Universal constructions ... Teaching category theory Idea Category theory is a toolset for describing the general abstract structures in mathematics Paradigm As opposed to set theory , category theory focuses not on elements x y – called object s – but on the relations between these objects: the ( homo morphism s between them x f y Later this will lead naturally on to an infinite sequence of steps: first 2-category theory which focuses on relation between relations, morphisms between morphisms:

60. Category Theory Math reference, an introduction to category theory. Category Theory, An Introduction Introduction Much of mathematics involves pattern recognition, followed by http://www.mathreference.com/cat,intro.html

Category Theory, An Introduction showHeader(1, "", "cat", "Category Theory", "func:Functors"); Introduction Much of mathematics involves pattern recognition, followed by generalization, then the swift application of the general to a problem that has not been seen before. Let me couch this in terms of computer programming, since I have been a professional programmer for 25 years. You write a ream of software to accomplish a certain task, and you feel like you've been here before. No, you didn't write this exact code before, line for line, but you wrote something very similar last year. You go back through your archives and dig out your old code. It does almost exactly what you want, with a few minor changes. You decide to write one program that handles both tasks. You'll need a couple parameters to accommodate the variations between tasks, but there is so much commonality; a dual-use program is the only way to go. You explain to your boss that you "Want to do it right." You want to build a flexible program that will handle both tasks. There will be less code over all, and fewer bugs, and if a bug is found, you can fix it once, not twice. But it will take a little longer to get the job done, because you're building a useful infrastructure, instead of solving today's problem as quickly as possible. You'll also need to run regression tests on the first task, to make sure the new program is handling it properly. That'll be another week, if nothing goes wrong. Your boss pulls out his gant chart and frowns. "I like your idea, but we can't slip schedule. I suggest you work weekends to make these changes. No - you won't be getting any additional compensation, but maybe I can sign you up for the Jelly of the Month club this Christmas. You know, that's the gift that keeps on giving the whole year through."

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