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1. CiteULike: Tag Cartesian_closed_category [2 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/cartesian_closed_category

Register Log in FAQ CiteULike News Discussion Journals Browse current issues Groups Search groups Tag cartesian_closed_category [2 articles] Recent papers classified by the tag cartesian_closed_category. Adjointness in foundations Repr. Theory Appl. Categ. , No. 16. (2006), pp. 1-16 (electronic). by William F Lawvere posted to logic adjunction by on 2007-10-09 10:28:35 as Diagonal arguments and Cartesian closed categories Repr. Theory Appl. Categ. , No. 15. (2006), pp. 1-13 (electronic). by William F Lawvere posted to incompleteness goedel diagonalization by on 2007-10-09 10:36:19 as Note: You may cite this page as: http://www.citeulike.org/tag/cartesian_closed_category RIS BibTeX RSS Related Tags Tags related to: cartesian_closed_category Filter: adjunction diagonalization goedel incompleteness ... logic CiteULike organises scholarly (or academic) papers or literature and provides bibliographic (which means it makes bibliographies) for universities and higher education establishments. It helps undergraduates and postgraduates. People studying for PhDs or in postdoctoral (postdoc) positions. The service is similar in scope to EndNote or RefWorks or any other reference manager like BibTeX, but it is a social bookmarking service for scientists and humanities researchers.

2. Cartesian Closed Category - Wikipedia, The Free Encyclopedia Retrieved from http//en.wikipedia.org/wiki/Cartesian_Closed_Category . Categories All articles with unsourced statements Articles with unsourced http://en.wikipedia.org/wiki/Cartesian_closed_category

var wgNotice = ""; var wgNoticeLocal = ""; var wgNoticeLang = "en"; var wgNoticeProject = "wikipedia"; Cartesian closed category From Wikipedia, the free encyclopedia Jump to: navigation search In category theory , a category is cartesian closed if, roughly speaking, any morphism defined on a product of two objects can be naturally identified with a morphism defined on one of the factors. These categories are particularly important in mathematical logic and the theory of programming . For generalizations of this notion to monoidal categories , see closed monoidal category Contents Definition Examples Applications Equational theory ... edit Definition The category C is called cartesian closed iff it satisfies the following three properties: it has a terminal object any two objects X and Y of C have a product X Y in C any two objects Y and Z of C have an exponential Z Y in C For the first two conditions above, it is the same to require that any finite (possibly empty) family of objects of C admit a product in C , because of the natural associativity of the categorical product and noticing that the empty product in a category is nothing but the terminal object of that category.

3. CARTESIAN CLOSED CATEGORIES And TOPOSES *) (* Including Programs cocomplete_category, complete_category, limit_examples, cc_category_of_sets, Cartesian_Closed_Category, category_with_products, category_with_coproducts http://www.cs.man.ac.uk/~david/categories/programs/topos

4. Cartesian Closed Category - Indopedia, The Indological Knowledgebase Retrieved from http//indopedia.org/Cartesian_Closed_Category.html . This page has been accessed 49 times. This page was last modified 2345, http://indopedia.org/Cartesian_closed_category.html

Indopedia Main Page FORUM Help ... Log in The Indology CMS Categories Category theory Printable version Wikipedia Article Cartesian closed category ज्ञानकोश: - The Indological Knowledgebase In category theory , a category is cartesian closed if, roughly speaking, any morphism defined on a product of two objects can be naturally identified with a morphism defined on one of the factors. These categories are particularly important in mathematical logic and the theory of programming . For generalizations of this notion, see monoidal category Contents showTocToggle("show","hide") 1 Definition 2 Examples 3 Applications 4 Equational theory ... edit Definition The category C is called cartesian closed iff it satisfies the following three properties: it has a terminal object any two objects X and Y of C have a product X Y in C for every object Y in C , the functor Y from C to C has a right adjoint Y , applied to the object Z , is written as HOM( Y Z Y Z or Z Y ; we will use the exponential notation in the sequel. The adjointness condition means that the set of morphisms in C from X Y to Z is naturally identified with the set of morphisms from X to Z Y , for any three objects X Y and Z in C edit Examples Examples of cartesian closed categories include: The category Set of all sets , with functions as morphisms, is cartesian closed. The product

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Contents Cartesian closed category In category theory , a category C is called cartesian closed if it satisfies the following three properties: it has a terminal object any two objects have a product for every object X in C , the functor X from C to C has a right adjoint X is usually denoted by HOM( X C from Y X to Z is naturally identified with the set of morphism from Y to HOM( X Z ), for any three objects X Y and Z in C The term "cartesian closed" is used because one thinks Y X as akin to the cartesian product of two sets. Examples Examples of cartesian closed categories include: The category Set of all sets , with functions as morphisms, is cartesian closed. The product Y X is the cartesian product of Y and X , and HOM( X Z ) is the set of all functions from X to Z . The adjointness is expressed by the following fact: the function f Y X Z is naturally identified with the function g Y X Z ) defined by g y x f y x ) for all x in X and y in Y The category of finite sets, with functions as morphisms, is cartesian closed for the same reason. If C is a small category, then the category of all functors from C to Set (with natural transformations as morphisms) is a cartesian closed category.

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Home Archaeology Astronomy Biology ... Current Article Cartesian closed category In category theory , a category is cartesian closed if, roughly speaking, any morphism defined on a product of two objects can be naturally identified with a morphism defined on one of the factors. These categories are particularly important in logic and the theory of programming. Table of contents showTocToggle("show","hide") 1 Definition 2 Examples 3 Applications 4 Equational theory Definition The category C is called cartesian closed iff it satisfies the following three properties: it has a terminal object any two objects X and Y of C have a product X Y in C for every object Y in C , the functor Y from C to C has a right adjoint Y , applied to the object Z , is written as HOM( Y Z Y Z or Z Y ; we will use the exponential notation in the sequel. The adjointness condition means that the set of morphisms in C from X Y to Z is naturally identified with the set of morphisms from X to Z Y , for any three objects X Y and Z in C The term "cartesian closed" is used because one thinks of Y X as akin to the cartesian product of two sets.

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11. Every Closed Category Is Enriched Over Itself - Sci.math.research | Google Group Try http//www.tac.mta.ca/tac/reprints/articles/10/tr10abs.html and http//en.wikipedia.org/wiki/Cartesian_Closed_Category . pg. Reply to author Forward http://groups.google.co.nz/group/sci.math.research/browse_thread/thread/4eeca867

Help Sign in sci.math.research Discussions ... Subscribe to this group This is a Usenet group - learn more every closed category is enriched over itself Options There are currently too many topics in this group that display first. To make this topic appear first, remove this option from another topic. There was an error processing your request. Please try again. Standard view View as tree Proportional text Fixed font messages Collapse all The group you are posting to is a Usenet group . Messages posted to this group will make your email address visible to anyone on the Internet. Your reply message has not been sent. Your post was successful sergei-akba...@rambler.ru View profile More options Aug 5, 8:33 pm Newsgroups: sci.math.research From: sergei-akba @rambler.ru Date: Sun, 05 Aug 2007 01:33:02 -0700 Local: Sun, Aug 5 2007 8:33 pm Subject: every closed category is enriched over itself Reply to author Forward Print Individual message ... Find messages by this author Dear colleagues, In one paper on category theory I found the following result: every closed category K is automatically enriched over K. I wonder how this

12. 000000 - Log Started Haskell/07.10.26 000017 Wli Mostly 025754 Cale http//en.wikipedia.org/wiki/Cartesian_Closed_Category Equational_theory hehe, check out the last equation 025755 lambdabot http://tunes.org/~nef/logs/haskell/07.10.26

00:00:00 - log: started haskell/07.10.26 00:00:17 Mostly to me, too, but I've got some cellular modem card that's bloze-only. 00:00:34 Subtext is getting pretty cool. 00:00:39 * hoelzro pats wli on the shoulder. 00:01:18 Cale: do you know the author of Subtext? Which Subtext are you speaking of, BTW? 00:01:28 http://subtextual.org/subtext2.html 00:01:29 Title: Created with Camtasia Studio 5 00:02:13 KatieHuber: where would I find info on calling haskell from C 00:02:14 ? 00:02:32 - join: iblechbot (n=iblechbo@45.4-dial.augustakom.net) joined #haskell 00:02:46 - quit: Khisanth ("Leaving") 00:02:48 Cale: I've been keeping an eye on that project 00:03:12 - join: Khisanth (n=Khisanth@68.237.97.161) joined #haskell 00:03:29 - join: andyjgill (n=andy@c-76-105-238-134.hsd1.or.comcast.net) joined #haskell 00:03:34 - join: filp (n=hordf@ip-168-248.sn2.eutelia.it) joined #haskell 00:03:52 nvm, I found something 00:04:03 thanks for all the help everyone! 00:04:06 - part: hoelzro left #haskell 00:04:11 ?where ffi 00:04:11

13. Index Cartesian CartesianProduct Cartesian_Coordinate_System Cartesian_Product Cartesian_Closed_Category Cartesian_coordinate Cartesian_coordinate_system http://www.newinreference.com/reference/ca/index.asp

ca CA CABG CAC CACM ... Ca?n_City,_Colorado

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Make eBroadcast my Homepage Contact Us It's Web Guide Encyclopedia Contents Cartesian closed category In category theory , a category C is called cartesian closed if it satisfies the following three properties: it has a terminal object any two objects have a product for every object X in C , the functor X from C to C has a right adjoint X is usually denoted by HOM( X C from Y X to Z is naturally identified with the set of morphism from Y to HOM( X Z ), for any three objects X Y and Z in C The term "cartesian closed" is used because one thinks Y X as akin to the cartesian product of two sets. Examples Examples of cartesian closed categories include: The category Set of all sets , with functions as morphisms, is cartesian closed. The product Y X is the cartesian product of Y and X , and HOM( X Z ) is the set of all functions from X to Z . The adjointness is expressed by the following fact: the function f Y X Z is naturally identified with the function g Y X Z ) defined by g y x f y x ) for all x in X and y in Y The category of finite sets, with functions as morphisms, is cartesian closed for the same reason. If C is a small category, then the category of all

16. Encyclopedia Sub-index Ca Cartesian_Closed_Category Cartesian_coordinate Cartesian_coordinate_system Cartesian_coordinates Cartesian_plain Cartesian_product Carthage http://www.freearchive.info/ca/

Index ca ca CA CABG CAC CACM ... Cañon_City,_Colorado Take this note to be able to access this article instantly from any page http://www.freearchive.info/./ca/index.html This article is licensed under the GNU Free Documentation License You may copy and modify it as long as the entire work (including additions) remains under this license. To view or edit this article at Wikipedia, follow this link Free Archive Home Up

17. Cartesian Closed Category - Cassiopedia, The True Encyclopedia Privacy policy; About Cassiopedia; Disclaimers; An uncorrected copy of this article might be available at en.wikipedia.org/wiki/Cartesian_Closed_Category. http://www.cassiopedia.org/wiki/index.php?title=Cartesian_closed_category

18. Karteziánská Uzavà ™ená Kategorie Karteziánská uzav ená kategorie. V teorii kategorie, kategorie je kartézský uzav ený jestliže, ost e mluvit, n jaké morphism definované na produktu dvou http://wikipedia.infostar.cz/c/ca/cartesian_closed_category.html

švodn­ str¡nka Tato str¡nka v origin¡le Kartezi¡nsk¡ uzavà ™en¡ kategorie V teorii kategorie , kategorie je kart©zsk½ uzavà ™en½ jestlià ¾e, ostà ™e mluvit, nějak© morphism definovan© na produktu dvou objektà ¯ mohou b½t pà ™irozeně identifikoval se s morphism definovan½m na jednom z faktorà ¯. Tyto kategorie jsou zvl¡à ¡tě dà ¯leà ¾it© v logice a teorii programov¡n­. Tabulka s obsahem showTocToggle("show","hide") 1 definice 2 pà ™­klady 3 aplikace 4 Equational teorie Definice Kategorie C je vol¡n kart©zsk½ uzavà ™en½ iff to uspokoj­ pokračov¡n­ tà ™i vlastnosti: to m¡ objekt termin¡lu nějak© dva objekty X a Y C m­t produkt X Y v C pro kaà ¾d½ objekt Y v C functor a bez; — Y od C k C m¡ prav½ adjoint Prav© adjoint a bez; — Y , platil o objektu Z , je ps¡n jako Hom ( Y Z Y Z nebo Z Y ; my budeme pouà ¾­vat exponenci¡ln­ z¡pis v pokračov¡n­. Adjointness podm­nka znamen¡ to soubor morphisms v C od X Y k Z je pà ™irozeně identifikoval se se souborem morphisms od X k Z Y , pro nějak© tà ™i objekty X Y a Z v C Term­n “kart©zsk½ uzavà ™en½â€ je pouà ¾­v¡n protoà ¾e jeden mysl­ na Y X jak bl­zk½ kart©zsk©mu součinu dvou souborà ¯.

19. Cartesian Closed Category - ExampleProblems.com Retrieved from http//www.exampleproblems.com/wiki/index. php/Cartesian_Closed_Category . Category Category theory. Views http://www.exampleproblems.com/wiki/index.php/Cartesian_closed_category

var skin = 'monobook';var stylepath = '/wiki/skins'; Cartesian closed category From ExampleProblems.com Jump to: navigation search In category theory , a category is cartesian closed if, roughly speaking, any morphism defined on a product of two objects can be naturally identified with a morphism defined on one of the factors. These categories are particularly important in mathematical logic and the theory of programming . For generalizations of this notion, see monoidal category Contents Definition Examples Applications Equational theory ... edit Definition The category C is called cartesian closed iff it satisfies the following three properties: it has a terminal object any two objects X and Y of C have a product X Y in C any two objects Y and Z of C have an exponential Z Y in C C admit a product in C , because of the natural associativity of the categorical product and noticing that the empty product in a category is nothing but the terminal object of that category. Y functor has a right adjoint Y Y for the functor from C to C that maps objects X to X Y Y ). This in turn, is expressed by the existence of a

20. Wikipedia Cartesian Closed Category The original article can be found at http//en.wikipedia. org/wiki/Cartesian_Closed_Category. All text is available under the terms of the GNU Free http://www.factbook.org/wikipedia/en/c/ca/cartesian_closed_category.html

Please Enter Your Search Term Below: only in factbook.org in the entire directory Websearch Directory Dictionary FactBook Wikipedia: Cartesian closed category Cartesian closed category From Wikipedia, the free encyclopedia. In category theory , a category is cartesian closed if, roughly speaking, any morphism defined on a product of two objects can be naturally identified with a morphism defined on one of the factors. These categories are particularly important in logic and the theory of programming. Definition The category C is called cartesian closed iff it satisfies the following three properties: it has a terminal object any two objects X and Y of C have a product X Y in C for every object Y in C , the functor Y from C to C has a right adjoint Y , applied to the object Z , is written as HOM( Y Z Y Z or Z Y ; we will use the exponential notation in the sequel. The adjointness condition means that the set of morphisms in C from X Y to Z is naturally identified with the set of morphisms from X to Z Y , for any three objects X Y and Z in C The term "cartesian closed" is used because one thinks of Y X as akin to the cartesian product of two sets.

21. Cartesian Closed Category http//medlibrary.org/medwiki/Cartesian_Closed_Category. All Wikipedia text is available under the terms of the GNU Free Documentation License. http://medlibrary.org/medwiki/Cartesian_closed_category

Welcome to the MedLibrary.org Wikipedia Supplement on Cartesian closed category Please Click to Return to Front Page We subscribe to the HONcode principles. Verify here Web medlibrary.org Cartesian closed category This MedLibrary.org supplementary page on Cartesian closed category is provided directly from the open source Wikipedia as a service to our readers. Please see the note below on authorship of this content, as well as the Wikipedia usage guidelines. To search for other content from our encyclopedia supplement, please use the form below: Related Sponsors In category theory , a category is cartesian closed if, roughly speaking, any morphism defined on a product of two objects can be naturally identified with a morphism defined on one of the factors. These categories are particularly important in mathematical logic and the theory of programming . For generalizations of this notion to monoidal categories , see closed monoidal category Contents Definition Examples Applications Equational theory ... References Definition The category C is called cartesian closed iff it satisfies the following three properties: it has a terminal object any two objects X and Y of C have a product X Y in C any two objects Y and Z of C have an exponential Z Y in C For the first two conditions above, it is the same to require that any finite (possibly empty) family of objects of

22. BrainDex The Knowledge Source - Free Online Encyclopedia - Cartesian Closed Cate Retrieved from http//www.braindex.com/encyclopedia/index. php/Cartesian_Closed_Category . Categories Category theory http://www.braindex.com/encyclopedia/index.php/Cartesian_closed_category

BrainDex Encyclopedia Forums Dictionary ... Free! Vacation on BrainDex Search Encyclopedia Classic Novels, Books and Literature Free Comprehensive Dictionary Online Free Worldwide Patent Search Free Newsletter More services, new products, and special offers! Subscribe to the FREE BrainDex.com Mailing List! Enter your email address here Please, enter email address In category theory , a category is cartesian closed if, roughly speaking, any morphism defined on a product of two objects can be naturally identified with a morphism defined on one of the factors. These categories are particularly important in mathematical logic and the theory of programming . For generalizations of this notion, see monoidal category Table of contents showTocToggle("show","hide") 1 Definition 2 Discussion 3 Examples 4 Applications ... 5 Equational theory Definition The category C is called cartesian closed iff it satisfies the following three properties: it has a terminal object any two objects X and Y of C have a product X Y in C for every object Y in C , the functor Y from C to C has a right adjoint Y , applied to the object Z , is written as HOM( Y Z Y Z or Z Y ; we will use the exponential notation in the sequel. The adjointness condition means that the set of morphisms in

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Create an account or log in Cartesian closed category Abelian group Computer science ... Tell a friend Navigation Main Page Current events Recent changes New pages ... Help Search Toolbox What links here Related changes Special pages Article ... Post Message Cartesian closed category From TheBestLinks.com In category theory , a category is cartesian closed if, roughly speaking, any morphism defined on a product of two objects can be naturally identified with a morphism defined on one of the factors. These categories are particularly important in mathematical logic and the theory of programming . For generalizations of this notion, see monoidal category Table of contents showTocToggle("show","hide") 1 Definition 2 Examples 3 Applications 4 Equational theory Definition The category C is called cartesian closed iff it satisfies the following three properties: it has a terminal object any two objects X and Y of C have a product X Y in C for every object Y in C , the functor Y from C to C has a right adjoint Y , applied to the object Z , is written as HOM( Y Z Y Z or Z Y ; we will use the exponential notation in the sequel. The adjointness condition means that the set of morphisms in

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var wgNotice = ""; var wgNoticeLocal = ""; var wgNoticeLang = "en"; var wgNoticeProject = "wikipedia"; Cartesian closed category From Wikipedia, the free encyclopedia Jump to: navigation search In category theory , a category is cartesian closed if, roughly speaking, any morphism defined on a product of two objects can be naturally identified with a morphism defined on one of the factors. These categories are particularly important in mathematical logic and the theory of programming . For generalizations of this notion to monoidal categories , see closed monoidal category Contents Definition Examples Applications Equational theory ... edit Definition The category C is called cartesian closed iff it satisfies the following three properties: it has a terminal object any two objects X and Y of C have a product X Y in C any two objects Y and Z of C have an exponential Z Y in C For the first two conditions above, it is the same to require that any finite (possibly empty) family of objects of C admit a product in C , because of the natural associativity of the categorical product and noticing that the empty product in a category is nothing but the terminal object of that category.

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Home About Us Options Support ... Futures Cartesian closed category Cartesian closed category Jump to: navigation search In category theory , a category is cartesian closed if, roughly speaking, any morphism defined on a product of two objects can be naturally identified with a morphism defined on one of the factors. These categories are particularly important in mathematical logic and the theory of programming . For generalizations of this notion to monoidal categories , see closed monoidal category Contents 1 Definition 2 Examples 3 Applications 4 Equational theory ... 5 References Definition The category C is called cartesian closed iff it satisfies the following three properties: it has a terminal object any two objects X and Y of C have a product X Y in C any two objects Y and Z of C have an exponential Z Y in C For the first two conditions above, it is the same to require that any finite (possibly empty) family of objects of C admit a product in C , because of the natural associativity of the categorical product and noticing that the empty product in a category is nothing but the terminal object of that category.

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Search Mathematics Encyclopedia and Lessons Lessons Popular Subjects algebra arithmetic calculus equations ... more References applied mathematics mathematical games mathematicians more ... Category theory Cartesian closed category In category theory , a category is cartesian closed if, roughly speaking, any morphism defined on a product of two objects can be naturally identified with a morphism defined on one of the factors. These categories are particularly important in mathematical logic and the theory of programming . For generalizations of this notion, see monoidal category Contents showTocToggle("show","hide") 1 Definition 2 Discussion 3 Examples 4 Applications ... 5 Equational theory Definition The category C is called cartesian closed iff it satisfies the following three properties: it has a terminal object any two objects X and Y of C have a product X Y in C for every object Y in C , the functor Y from C to C has a right adjoint Y , applied to the object Z , is written as HOM( Y Z Y Z or Z Y ; we will use the exponential notation in the sequel. The adjointness condition means that the set of morphisms in C from X Y to Z is naturally identified with the set of morphisms from X to Z Y , for any three objects X Y and Z in C Discussion For people who don't have a feel for how adjoints work, another way of formulating the third condition is that for any two objects

29. Article About "Cartesian Closed Category" In The English Wikipedia On 24-Apr-200 The Cartesian closed category reference article from the English Wikipedia on 24Apr-2004 (provided by Fixed Reference snapshots of Wikipedia from http://fixedreference.org/en/20040424/wikipedia/Cartesian_closed_category

The Cartesian closed category reference article from the English Wikipedia on 24-Apr-2004 (provided by Fixed Reference : snapshots of Wikipedia from wikipedia.org) Cartesian closed category In category theory , a category is cartesian closed if, roughly speaking, any morphism defined on a product of two objects can be naturally identified with a morphism defined on one of the factors. These categories are particularly important in logic and the theory of programming. Table of contents showTocToggle("show","hide") 1 Definition 2 Examples 3 Applications 4 Equational theory Definition The category C is called cartesian closed iff it satisfies the following three properties: it has a terminal object any two objects X and Y of C have a product X Y in C for every object Y in C , the functor Y from C to C has a right adjoint Y , applied to the object Z , is written as HOM( Y Z Y Z or Z Y ; we will use the exponential notation in the sequel. The adjointness condition means that the set of morphisms in C from X Y to Z is naturally identified with the set of morphisms from X to Z Y , for any three objects X Y and Z in C The term "cartesian closed" is used because one thinks of Y X as akin to the cartesian product of two sets.

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Web www.physicsdaily.com Categories Category theory Cartesian closed category In category theory , a category is cartesian closed if, roughly speaking, any morphism defined on a product of two objects can be naturally identified with a morphism defined on one of the factors. These categories are particularly important in mathematical logic and the theory of programming . For generalizations of this notion, see monoidal category Contents showTocToggle("show","hide") 1 Definition 2 Discussion 3 Examples 4 Applications ... 5 Equational theory Definition The category C is called cartesian closed iff it satisfies the following three properties: it has a terminal object any two objects X and Y of C have a product X Y in C for every object Y in C , the functor Y from C to C has a right adjoint Y , applied to the object Z , is written as HOM( Y Z Y Z or Z Y ; we will use the exponential notation in the sequel. The adjointness condition means that the set of morphisms in C from X Y to Z is naturally identified with the set of morphisms from X to Z Y , for any three objects X Y and Z in C Discussion For people who don't have a feel for how adjoints work, another way of formulating the third condition is that for any two objects

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Periodic Table standard table large table Chemical Elements ... Category theory Cartesian closed category In category theory , a category is cartesian closed if, roughly speaking, any morphism defined on a product of two objects can be naturally identified with a morphism defined on one of the factors. These categories are particularly important in mathematical logic and the theory of programming . For generalizations of this notion, see monoidal category Contents showTocToggle("show","hide") 1 Definition 2 Discussion 3 Examples 4 Applications ... 5 Equational theory Definition The category C is called cartesian closed iff it satisfies the following three properties: it has a terminal object any two objects X and Y of C have a product X Y in C for every object Y in C , the functor Y from C to C has a right adjoint Y , applied to the object Z , is written as HOM( Y Z Y Z or Z Y ; we will use the exponential notation in the sequel. The adjointness condition means that the set of morphisms in C from X Y to Z is naturally identified with the set of morphisms from X to Z Y , for any three objects X Y and Z in C Discussion For people who don't have a feel for how adjoints work, another way of formulating the third condition is that for any two objects

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Guajara in other languages: Spanish Deutsch French Italian Cartesian closed category In category theory , a category is cartesian closed if, roughly speaking, any morphism defined on a product of two objects can be naturally identified with a morphism defined on one of the factors. These categories are particularly important in logic and the theory of programming. Table of contents showTocToggle("show","hide") 1 Definition 2 Examples 3 Applications 4 Equational theory Definition The category C is called cartesian closed iff it satisfies the following three properties: it has a terminal object any two objects X and Y of C have a product X Y in C for every object Y in C , the functor Y from C to C has a right adjoint Y , applied to the object Z , is written as HOM( Y Z Y Z or Z Y ; we will use the exponential notation in the sequel. The adjointness condition means that the set of morphisms in C from X Y to Z is naturally identified with the set of morphisms from X to Z Y , for any three objects X Y and Z in C The term "cartesian closed" is used because one thinks of Y X as akin to the cartesian product of two sets.

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[x] Close ad CARTESIAN CLOSED CATEGORY In category theory , a category is cartesian closed if, roughly speaking, any morphism defined on a product of two objects can be naturally identified with a morphism defined on one of the factors. These categories are particularly important in mathematical logic and the theory of programming . For generalizations of this notion to monoidal categories , see closed monoidal category Contents Definition Examples Applications Equational theory Definition The category C is called cartesian closed iff it satisfies the following three properties: it has a terminal object any two objects X and Y of C have a product X Y in C any two objects Y and Z of C have an exponential Z Y in C For the first two conditions above, it is the same to require that any finite (possibly empty) family of objects of C admit a product in C , because of the natural associativity of the categorical product and noticing that the empty product in a category is nothing but the terminal object of that category. For the third condition it is equivalent to ask that the functor Y (i.e. the functor from

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Navigation Home Recent Popular Blog ... Statistics Help Suggestions Contact Us How to Edit Help google_ad_client = "pub-2996456105980425"; //120x600, created 12/8/07 google_ad_slot = "3475401235"; google_ad_width = 120; google_ad_height = 600; google_color_border = "FFFFFF"; google_color_bg = "FFFFFF"; //google_color_link = "F49426"; google_color_link = "BF8C40"; google_color_text = "000000"; google_color_url = "BAD757"; [Edit] In category theory , a category is cartesian closed if, roughly speaking, any morphism defined on a product of two objects can be naturally identified with a morphism defined on one of the factors. These categories are particularly important in mathematical logic and the theory of programming . For generalizations of this notion to monoidal categories , see closed monoidal category Cartesian closed category Definition Examples ... top Definition The category C is called cartesian closed iff it satisfies the following three properties: it has a terminal object any two objects X and Y of C have a product X Y in C any two objects Y and Z of C have an exponential Z Y in C For the first two conditions above, it is the same to require that any finite (possibly empty) family of objects of

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var skin = 'monobook';var stylepath = '/w/skins'; Views Cartesian closed category Jump to: navigation search In category theory , a category is cartesian closed if, roughly speaking, any morphism defined on a product of two objects can be naturally identified with a morphism defined on one of the factors. These categories are particularly important in mathematical logic and the theory of programming . For generalizations of this notion to monoidal categories , see closed monoidal category Definition Examples Applications ... References Definition The category C is called cartesian closed iff it satisfies the following three properties: it has a terminal object any two objects X and Y of C have a product X Y in C any two objects Y and Z of C have an exponential Z Y in C For the first two conditions above, it is the same to require that any finite (possibly empty) family of objects of C admit a product in C , because of the natural associativity of the categorical product and noticing that the empty product in a category is nothing but the terminal object of that category.

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US states Yellow Pages Explore Categories/Topics Auto ... Feedback NEWS UPDATES In category theory , a category is cartesian closed if, roughly speaking, any morphism defined on a product of two objects can be naturally identified with a morphism defined on one of the factors. These categories are particularly important in mathematical logic and the theory of programming . For generalizations of this notion to monoidal categories , see closed monoidal category Contents Definition Examples Applications Equational theory Definition The category C is called cartesian closed iff it satisfies the following three properties: it has a terminal object any two objects X and Y of C have a product X Y in C any two objects Y and Z of C have an exponential Z Y in C For the first two conditions above, it is the same to require that any finite (possibly empty) family of objects of C admit a product in C , because of the natural associativity of the categorical product and noticing that the empty product in a category is nothing but the terminal object of that category. For the third condition it is equivalent to ask that the functor Y (i.e. the functor from

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Home Browse articles alphabetically: A B C D ... Z Enter your search terms Submit search form Web www.wikilookup.info Kelvin Brown's Wiki Cartesian closed category In category theory , a category is cartesian closed if, roughly speaking, any morphism defined on a product of two objects can be naturally identified with a morphism defined on one of the factors. These categories are particularly important in logic and the theory of programming. Table of contents showTocToggle("show","hide") 1 Definition 2 Examples 3 Applications 4 Equational theory Definition The category C is called cartesian closed iff it satisfies the following three properties: it has a terminal object any two objects X and Y of C have a product X Y in C for every object Y in C , the functor Y from C to C has a right adjoint Y , applied to the object Z , is written as HOM( Y Z Y Z or Z Y ; we will use the exponential notation in the sequel. The adjointness condition means that the set of morphisms in C from X Y to Z is naturally identified with the set of morphisms from X to Z Y , for any three objects X Y and Z in C The term "cartesian closed" is used because one thinks of Y X as akin to the cartesian product of two sets.

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Wacklepedia Home Page Index Cartesian closed category From Wacklepedia - The Free Encyclopedia In category theory , a category is cartesian closed if, roughly speaking, any morphism defined on a product of two objects can be naturally identified with a morphism defined on one of the factors. These categories are particularly important in logic and the theory of programming. Table of contents 1 Definition 2 Examples 3 Applications 4 Equational theory Definition The category C is called cartesian closed iff it satisfies the following three properties: it has a terminal object any two objects X and Y of C have a product X Y in C for every object Y in C , the functor Y from C to C has a right adjoint Y , applied to the object Z , is written as HOM( Y Z Y Z or Z Y ; we will use the exponential notation in the sequel. The adjointness condition means that the set of morphisms in C from X Y to Z is naturally identified with the set of morphisms from X to Z Y , for any three objects X Y and Z in C The term "cartesian closed" is used because one thinks of Y X as akin to the cartesian product of two sets.

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