21. Portal:Category Theory - Wikipedia, The Free Encyclopedia Wikipedia portals Culture Geography Health History Mathematics Natural sciences People Philosophy Religion Society Technology http://en.wikipedia.org/wiki/Portal:Category_theory

Portal:Category theory From Wikipedia, the free encyclopedia Jump to: navigation search Wikipedia portals Culture ... edit Category theory 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 The term " abstract nonsense " has been used by some critics to refer 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'. Topos theory is a form of abstract sheaf theory , with geometric origins, and leads to ideas such as pointless topology Show new selections edit Selected Article In category theory , the derived category of an Abelian category is a construction of homological algebra introduced to refine and in a certain sense to simplify the theory of derived functors . The development of the theory, by

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24. Aspuru-Guzik Research Group - Category Theory Category theory naturally arises when faced with developing new mathematics and new logics and is also crucial in understanding existing structures. http://aspuru.chem.harvard.edu/People/Jacob_D._Biamonte/Category_Theory/

About Alan Research Publications People ... Calendar News: On December 10th, 2007 we created a wiki/blog for the new seminar series, Categories Logic and Foundations of Physics ( link ). We also have a facebook group The theory of categories has come to occupy a central position in contemporary mathematics and theoretical computer science, and in particular, mathematical physics. Category theory naturally arises when faced with developing new mathematics and new logics and is also crucial in understanding existing structures. Category theory online video collection Catsters youtube channel What is a category? List of category theory topics ... Categories mailing list Online textbooks: Categories, Types and Structures. An introduction to Category Theory for the working computer scientist , Andrea Asperti and Giuseppe Longo. A Categorical Primer A gentle introduction to category theory , Maarten M. Fokkinga. An introduction to the theory of categories , David Madore. This is a list of Peter Selinger's papers, along with abstracts and hyperlinks. Linear Logic In mathematical logic, linear logic is a type of 'resource sensitive' logic that has interesting ties to the theory of computation and category theory. It borrows some ideas from

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28. Retract_(category_theory) Encyclopedia Topics | Reference.com Encyclopedia article of Retract_(category_theory) at Reference.com compiled from comprehensive and current sources. http://www.reference.com/browse/Retract_(category_theory)

29. Wapedia - Wiki: Adjoint Functors It is studied in generality by the branch of mathematics known as category theory, which helps to minimize the repetition of the same logical details http://wapedia.mobi/en/Counit_(category_theory)

Wiki: Adjoint functors "Adjunction" redirects here. For the construction in field theory, see Adjunction (field theory) In mathematics adjoint functors are pairs of functors which stand in a particular relationship with one another, called an adjunction . The relationship of adjunction is ubiquitous in mathematics, as it rigorously reflects the intuitive notions of optimization and efficiency. It is studied in generality by the branch of mathematics known as category theory , which helps to minimize the repetition of the same logical details separately in every subject. In the most concise symmetric definition, an adjunction between categories C and D is a pair of functors, and and a family of bijections which is natural in the variables X and Y . The functor F is called a left adjoint functor , while G is called a right adjoint functor . The relationship “ F is left adjoint to G ” (or equivalently, “ G is right adjoint to F ”) is sometimes written This definition and others are made precise below. Contents: 1. Introduction

30. Science > Mathematics > Category Theory ABOUT POINTERS 18 Category theory, homological algebra Introduction Category theory, a comparatively new field of mathematics, provides a universal http://www.einet.net/directory/14819/Category_Theory.htm

31. Category Theory - Mathematics Pages in category Category theory . The following 2 pages are in this category, Retrieved from http//math.wikia.com/wiki/Categorycategory_theory http://math.wikia.com/wiki/Category:Category_theory

Wikia Skip to Content Skip to Wiki Navigation Skip to Site Navigation Wikia Navigation Start a wiki Entertainment Fall TV Glee ... Mathematics Mathematics Navigation Browse content Category list Mathematics Project pages ... Geometry Random Page Wiki Activity Watchlist Recent changes Talk Category theory Edit Category page Pages in category "Category theory" The following 2 pages are in this category, out of 2 total. C Category theory M Monoid Media in category "Category theory" The following 3 files are in this category, out of 3 total. Alf0.PNG 18,102 bytes Alf1.PNG 19,218 bytes Alf2.PNG 19,139 bytes Retrieved from " http://math.wikia.com/wiki/Category:Category_theory Related Categories Categories Mathematics Structure Add category Pages on Mathematics Create a Page pages on this wiki Recent Wiki Activity Kjhf edited Main Page 1 day ago A Wikia contributor edited Formula for Area Bounded by a Circle/Proof 6 days ago A Wikia contributor created Numerator A Wikia contributor created Mass See more > Latest Photos Add a Photo photos on this wiki by 8. Juni

32. Cramster - Definition Of Limit (category Theory) In category theory, a branch of mathematics, the abstract notion of a limit captures the essential properties of universal constructions that are used in http://www.cramster.com/reference/wiki.aspx?wiki_name=Limit_(category_theory)

33. Limit (category Theory) Glasglow Research Project In category theory, the limit of a functor generalizes the notions of inverse limit and product used in various parts of mathematics. http://www.glasglow.com/e2/li/Limit_(category_theory).html

Contents Limit (category theory) 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 F If J is a small category and every functor from J to C has a limit, then the limit operation forms a functor from the functor category (see category theory C J to C . For example, if J is a discrete category and C is the category Ab of abelian groups, then lim :

34. Category Theory Summary | BookRags.com Category theory. Category theory summary with 11 pages of encyclopedia entries, research information, and more. http://www.bookrags.com/wiki/Category_theory

35. Dual (category Theory) In category theory, an abstract branch of mathematics, the dual category or opposite category Cop of a category C is the category formed by reversing all http://www.worldlingo.com/ma/enwiki/en/Dual_(category_theory)

Mul tili ngual Ar chi ve Po wer ed by Wor ldLi ngo Dual (category theory) Home Multilingual Archive Index Ch oo se your la ngua ge: English Italiano Deutsch Nederlands ... Svenska var addthis_pub="anacolta"; Dual (category theory) In category theory , an abstract branch of mathematics , the dual category or opposite category C op of a category C is the category formed by reversing all the morphisms of C . That is, we take C op to be the category with objects that are those of C , but with the morphisms from X to Y in C op being the morphisms from Y to X in C . Hence, the dual category of the dual category of a category is the original category itself. Contents Examples Formal definition Duality Dualities ... See also Examples An example comes from reversing the direction of inequalities in a partial order . So if X is a set and ≤ a partial order relation, we can define a new partial order relation ≤ new by x new y if and only if y x For example, there are opposite pairs child/parent, or descendant/ancestor. The category of Boolean algebras and Boolean homomorphisms can be shown to be the opposite of the category of Stone spaces and continuous functions.

36. Category:Category Theory - MyWikiBiz, Author Your Legacy Pages in category Category Theory . The following 2 pages are in this category, Retrieved from http//www.mywikibiz.com/Categorycategory_theory http://www.mywikibiz.com/Category:Category_Theory

Quickly add a free MyWikiBiz directory listing! Category:Category Theory MyWikiBiz, Author Your Legacy — Sunday October 31, 2010 Jump to: navigation search Category Theory Pages in category "Category Theory" The following 2 pages are in this category, out of 2 total. C Cybernetics T Tacit extension Retrieved from " http://www.mywikibiz.com/Category:Category_Theory Views Category Discussion View source History Personal tools Log in / create account Navigation Main page Add a listing Directory portals Recent changes ... Site Stats semantic SEO methods Properties Categories Search Toolbox What links here Related changes Special pages Printable version ... Browse properties This page was last modified on 18 May 2007, at 16:54. This page has been accessed 1,021 times. Your cash donation, though not tax-deductible, helps us offset hosting and bandwidth costs. MyWikiBiz has surpassed several important milestones: over 3,000 registered editors over 60,000 pages over 680,000 unique visitors over 1,200,000 page loads According to Alexa, we reach more Internet users than the Brazilian government's website and the home page of the 10th largest American company. Amazing, but

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38. Category Theory - On Opentopia, Find Out More About Category Theory In mathematics, category theory deals in an abstract way with mathematical structures and relationships between them. It is halfjokingly known as generalized abstract nonsense http://encycl.opentopia.com/term/Category_theory

About Opentopia Opentopia Directory Encyclopedia ... Tools Category theory Encyclopedia C CA CAT : Category theory In mathematics category theory 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, 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 1945, in connection with algebraic topology See Category theory topics for a breakdown of relevant articles. Contents 1 Background 2 Historical notes 3 Categories, objects, and morphisms 3.1 Some properties of morphisms ... 13 External links 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 set s G endowed with a binary operation satisfying a certain set of axiom s. One can proceed to

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siia. For more information, visit www. structures full , is a unique program, which recognizes pioneers who leverage technology to address the world's most pressing challenges.thetech. applied 1995 The curriculum will now enter the Codie Awards Finalists Review Program to be judged by members of the SIIA to determine a winner in each category. ADVISORY/April 4 Nomination Deadline for 2005 Tech Museum Awards; Global Awards Program Recognizes Those Who Use Technology to Benefit Humanity , Santa Clara University 's Center for Science, Technology, and Society, the United Nations Development Programme and The World Bank Institute. category applied Winners will be announced at the 20th Annual Codie Awards Gala on May 25, 2005 at Universal Studio's Globe Theater in Universal City, CA. Established in 1998 by researchers , teachers and scholars from Carnegie Mellon University, Carnegie Learning was founded to apply and extend more than 20 years of award-winning research in cognitive science to mathematics instruction . The Tech Museum of Innovation WHAT The deadline to nominate for the 2005 Tech Museum Awards is April vol structures algebra science science structures asp About Carnegie Learning Carnegie Learning is the developer of the Cognitive Tutor(R) comprehensive curricula for secondary mathematics.

40. Category Theory : Universal Constructions Limits And Colimits Category theory Universal Constructions Limits And Colimits images, discuss, define, news. http://www.servinghistory.com/topics/category_theory::sub::Universal_Constructio

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