1. Category Theory - Wikipedia, The Free Encyclopedia Retrieved from http//en.wikipedia.org/wiki/category_theory . Categories Category theory Higher category theory. Views http://en.wikipedia.org/wiki/Category_theory

Category theory From Wikipedia, the free encyclopedia Jump to: navigation search In mathematics category theory deals in an abstract way with mathematical structures and relationships between them. Categories now 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 1942-1945, in connection with algebraic topology Category theory has several faces known not just to specialists, but to other mathematicians. " General abstract nonsense " refers, perhaps not entirely affectionately, to its high level of abstraction, compared to more classical branches of mathematics. Homological algebra is category theory in its aspect of organising and suggesting calculations in abstract algebra Diagram chasing is a visual method of arguing with abstract 'arrows', and has appeared in a Hollywood film, as Jill Clayburgh proved the snake lemma (at the start of It's My Turn Topos theory is a form of abstract sheaf theory , with geometric origins, and leads to ideas such as pointless topology Category theory Portal Contents Background Historical notes Categories, objects and morphisms

2. Category_theory: Blogs, Photos, Videos And More On Technorati Mentions by Day. Posts tagged category_theory per day for the past 30 days. Chart of results for category_theory. See your posts here http://technorati.com/tag/category_theory

Check out the buzz in Technology Join Sign in Help ... Small Business Up Entertainment Main TV Music ... Gaming Up Lifestyle Main Autos Family ... Travel Up Politics Sports Technology Main ... IT Up Blogs Photos Videos Blogger Central ... Developers Up 67 posts tagged Subscribe Posts Blogs Photos Videos search in entire post tags only of blogs with any authority a little authority some authority a lot of authority in language all languages Arabic (العربية) Chinese (中文) Dutch (Nederlands) English French (Fran§ais) German (Deutsch) Greek (Ελληνικά) Hebrew (עברית) Italian (Italiano) Japanese (日本語) Korean (한국어) Norwegian (Norsk) Persian (فارسی) Polish (Polski) Portuguese (Portuguªs) Russian (Русский) Spanish (Espa±ol) Swedish (Svenska) Turkish (T¼rk§e) Vietnamese (Tiếng Việt) Categorical Information Theory http://www.sunclipse.org/ ?p=607 Categorical Information Theory • No Comments 27 March 2008 by Blake Stacey Ben Allen is now on the arXivotubes, with a category-theoretic arithmetic of information. The concept of information has found application across the sciences. 3 days ago by blakestacey in Science After Sunclipse Authority: 114 Derived categories bleg http://sbseminar.wordpress.com/ 2008/ 03/ 24/ derived-categories-bleg/

3. CiteULike: Tag Category_theory [70 Articles] posted to incompleteness goedel _file diagonalization _copy category_theory cartesian_closed_category by adrian_pigors on 200710-09 103619 as http://www.citeulike.org/tag/category_theory

Register Log in FAQ Sponsored link CiteULike News CiteGeist Discussion Journals Browse current issues Groups Search groups Tag category_theory [70 articles] Recent papers classified by the tag category_theory. A Category Theory Approach to Conceptual Data Modeling Informatique Theorique et Applications , Vol. 30, No. 1. (1996), pp. 31-79. by E Lippe , AHMt Arthur posted to by yagermadden on 2005-04-22 18:06:50 as along with 2 people and 1 group pilho jolilius TUCS-ES_Lab ... Functorial Semantics of Rewrite Theories Lecture Notes in Computer Science : Formal Methods in Software and Systems Modeling (2005), pp. 220-235. Meseguer posted to by xiemaisi on 2006-12-12 07:41:31 as along with 1 group AS-IIS_ReadingGroup Conditional rewriting logic as a unified model of concurrency Theor. Comput. Sci. , Vol. 96, No. 1. (April 1992), pp. 73-155. Meseguer posted to maude by xiemaisi on 2006-12-12 07:39:05 as along with 1 person and 1 group kavabean AS-IIS_ReadingGroup Generalised algebraic theories and contextual categories Annals of Pure and Applied Logic , Vol. 32 (1986), pp. 209-243.

4. Arrows-category_theory - SWiK sorted by recent see popular. Content Tagged with arrows + category_theory Programming haskell Papers arrows fp monads category_theory fplang http://swik.net/arrows category_theory

SWiK login / register changes) Your tags: or Cancel New Page Wiki RSS Feed Blog Bookmarks Enter RSS URL to Syndicate here: (Feed found, click Add Page to syndicate.) Error finding feed, please try again A Blog Page allows you to add entries, for news or other time sensitive postings A Bookmarks page is a really simple list of links - ordered by date. Enter a title for this page this list of links the feed this blog Formatting help Login required to save to your tagged pages.) Add to your tagged pages? Enter space separated tags: (or Cancel var g_swipEditType = 'wiki'; var g_swipChangeType = 'wiki'; Wiki Page Open Source Project Finding project information from the web - complete. Preview Formatting Preview your edits: Make further edits (or Cancel Homepage Author License Login required to save to your tagged pages.)

5. Haskell/Category Theory - Wikibooks, Collection Of Open-content Textbooks Retrieved from http//en.wikibooks.org/wiki/Haskell/category_theory . Subject Haskell. Views. Module Discussion Edit this page History http://en.wikibooks.org/wiki/Haskell/Category_theory

Haskell/Category theory From Wikibooks, the open-content textbooks collection Haskell Jump to: navigation search Category theory Solutions Contents Introduction to categories Category laws Hask, the Haskell category Functors ... Notes Wider Theory Denotational semantics Equational reasoning Program derivation Category theory The Curry-Howard isomorphism edit this chapter This article attempts to give an overview of category theory, insofar as it applies to Haskell. To this end, Haskell code will be given alongside the mathematical definitions. Absolute rigour is not followed; in its place, we seek to give the reader an intuitive feel for what the concepts of category theory are and how they relate to Haskell. edit Introduction to categories A simple category, with three objects A B and C , three identity morphisms i d A i d B and i d C , and two other morphisms and . The third element (the specification of how to compose the morphisms) is not shown. A category is, in essence, a simple collection. It has three components: A collection of objects A collection of morphisms , each of which ties two objects (a source object and a target object ) together. (These are sometimes called

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7. Category Theory/Natural Transformation - HaskellWiki Retrieved from http//www.haskell.org/haskellwiki/category_theory/ Natural_transformation . This page has been accessed 802 times. http://www.haskell.org/haskellwiki/Category_theory/Natural_transformation

Haskell Wiki community Recent changes Random page ... Special pages Not logged in Log in Help Edit this page Discuss this page ... Related changes Category theory/Natural transformation Category theory Categories Theoretical foundations map ... even maybeToList Just yields the same as maybeToList fmap even Just yields: both yield False In the followings, this example will be used to illustrate the notion of natural transformation. If the examples are exaggerated and/or the definitions are incomprehensible, try #External links Contents Definition Example: maybeToList Vertical arrows: sides of objects Left: side of X object ... edit 1 Definition Let denote categories. Let be functors. Let . Let Let us define the natural transformation. It associates to each object of a morphism of in the following way (usually, not sets are discussed here, but proper classes, so I do not use term “function” for this mapping): . We call A the component of at A Thus, the following diagram commutes (in edit 2 Example: maybeToList As already mentioned map even maybeToList Just yields the same as maybeToList fmap even Just yields: both yield False This example will be shown in the light of the above definition in the followings.

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9. Index Of /paper/l/lecture_notes/murfet-category_theory . Parent Directory, -. DerivedFunctors.pdf, 11-Jan-2007 1435......Index of /paper/l/lecture_notes/murfetcategory_theory. Name, Last modified, Size, http://www.ajorza.org/paper/l/lecture_notes/murfet-category_theory/

Index of /paper/l/lecture_notes/murfet-category_theory Name Last modified Size Description ... DerivedFunctors.pdf 11-Jan-2007 14:35 Dimensions.pdf 11-Jan-2007 14:35 Ext.pdf 11-Jan-2007 14:35 Tor.pdf 11-Jan-2007 14:35 Apache/2.2.3 (Mandriva Linux/PREFORK-1mdv2007.0) Server at www.ajorza.org Port 80

10. Category_theory [the Libarynth] category_theory.txt · Last modified 2007/06/08 1850 (external edit). Recent changes RSS feed Creative Commons License Subsidise our existence. http://lib.fo.am/category_theory

the libarynth Trace: Category Theory http://plato.stanford.edu/entries/category-theory/ Category theory is a general mathematical theory of structures and sytems of structures. It allows us to see, among other things, how structures of different kinds are related to one another as well as the universal components of a family of structures of a given kind. The theory is philosophically relevant in more than one way. For one thing, it is considered by many as being an alternative to set theory as a foundation for mathematics. Furthermore, it can be thought of as constituting a theory of concepts. Finally, it sheds a new light on many traditional philosophical questions, for instance on the nature of reference and truth. http://math.ucr.edu/home/baez/categories.html reading “Basic Category Theory for Computer Scientists”, Benjamin C. Pierce “A Categorical Manifesto” by Goguen http://citeseer.nj.nec.com/goguen91categorical.html http://www.let.uu.nl/esslli/Courses/barr-wells.html http://scienceblogs.com/goodmath/goodmath/category_theory/

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var skin = 'monobook';var stylepath = '/ontowiki/skins'; Category theory From CoreOntoWiki Jump to: navigation search category_theory ì¹´í Œê³ ë¦¬ë¡  Inspec edit Taxonomic relation is subclass of: is superclass of: edit Non-taxonomic Relation has relations of: mathematics edit See also at wikiPedia Retrieved from " http://korterm.kaist.ac.kr/ontowiki/index.php/Category_theory Views Article Discussion Edit History Personal tools Log in / create account CoreOnto ITDeviceOntology -byKAIST -byYU -byPosTech ... ITPersonOntology Navigation Main Page Community portal Current events Recent changes ... Donations Search Toolbox What links here Related changes Special pages Printable version ... Permanent link This page was last modified 13:00, 8 April 2007. This page has been accessed 6 times. About CoreOntoWiki

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Arts Business Computers Games ... ABOUT Options: Directory Entire Web Top Science Math Algebra Category Theory Events Journals Research Groups Top/Games/Card Games/Special Decks/Ccard ... Paul Taylor's Home Page - Includes papers on category theory. http://www.cs.man.ac.uk/~pt/ Groupoids - Notes by Ronald Brown. http://www.bangor.ac.uk/~mas010/gpds.htm Groupoid Home Page - Maintained by Birant Ramazan. Address book, open problems, meetings, pictures, other resources. http://unr.edu/homepage/ramazan/groupoid/ Higher-Dimensional Categories - An illustrated guide book by Eugenia Cheng and Aaron Lauda (PS/PDF). http://www.dpmms.cam.ac.uk/~elgc2/guidebook/ Computational Category Theory - 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/ CT Category Theory - Section of the e-print arXiv dealing with category theory, including such topics as: enriched categories, topoi, abelian categories, monoidal categories, homological algebra. http://front.math.ucdavis.edu/math.CT

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Novi upisi Hot Top Nas Izbor ... DIR Search: search the entire directory search this category only Top Science Math Algebra ... Research Groups See also: Games: Card Games: Special Decks: Ccard Science: Math: Logic and Foundations Science: Math: Topology: Algebraic Topology Categorical Myths and Legends - An archive of stories about category theorists. Categories Home Page - Web page for the category theory mailing list. Categories, Quantization, and Much More - Introductory article by John Baez. Category Theory - This expository article is an entry in the Stanford Encyclopedia of Philosophy. Category Theory and Homological Algebra - In the "known maths" series. Computational Category Theory - An implementation of concepts and constructions from category theory in the functional programming language Standard ML. Documentation and code. CT Category Theory - Section of the e-print arXiv dealing with category theory, including such topics as: enriched categories, topoi, abelian categories, monoidal categories, homological algebra. Descent and Category Theory Connections - Maintained by M. Alsani.

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