User contributions for Vipul
10 December 2008
- 00:0100:01, 10 December 2008 diff hist +137 Category of topological spaces No edit summary
9 December 2008
- 23:5623:56, 9 December 2008 diff hist +356 N Category of topological spaces New page: {{particular category}} ==Definition== The '''category of topological spaces''', denoted <math>\operatorname{Top}</math>, is defined as follows: * Its objects are topological spaces...
- 23:5423:54, 9 December 2008 diff hist +194 N Template:Particular category New page: {{quotation|''This article is about a particular category''<br>View other particular categories}}<includeonly>Category:Particular categories</includ... current
- 23:5323:53, 9 December 2008 diff hist +366 N Category of groups New page: {{particular category}} ==Definition== The '''category of groups''', denoted <math>\operatorname{Group}</math> or <math>\operatorname{Grp}</math>, is defined as follows: * Its objects a...
- 23:4423:44, 9 December 2008 diff hist +524 N Category of sets New page: ==Definition== The '''category of sets''', denoted <math>\operatorname{Set}</math>, is defined as follows: * The objects of this category are sets. * For any two sets <math>A,B</math...
- 23:4223:42, 9 December 2008 diff hist +1,001 N Natural isomorphism New page: {{basicdef}} ==Definition== ===Symbol-free definition=== A '''natural isomorphism''' between functors is a natural transformation between the functors that has a two-sided inverse w... current
- 23:3623:36, 9 December 2008 diff hist +21 N Covariant functor Redirecting to Functor current
- 23:3623:36, 9 December 2008 diff hist +529 N Representable contravariant functor New page: ==Definition== Suppose <math>\mathcal{C}</math> is a category and <math>\mathcal{F}:\mathcal{C} \to \operatorname{Set}</math> is a contravariant functor to the [[category of sets]... current
- 23:3323:33, 9 December 2008 diff hist +34 N Template:Proofat New page: ''For full proof, refer: {{{1}}}'' current
- 23:3323:33, 9 December 2008 diff hist +1,194 N Covariant Hom functor New page: ==Definition== Suppose <math>\mathcal{C}</math> is a category and <math>A \in \operatorname{Ob}\mathcal{C}</math>. The '''covariant Hom functor''' corresponding to <math>A</math> is d...
- 23:2823:28, 9 December 2008 diff hist +627 N Representable functor New page: ==Definition== Suppose <math>\mathcal{C}</math> is a category, and <math>\mathcal{F}: \mathcal{C} \to \operatorname{Set}</math> is a functor. In other words, <math>\mathcal{F}</ma... current
- 23:2523:25, 9 December 2008 diff hist +382 Category No edit summary current
- 23:2223:22, 9 December 2008 diff hist +132 Functor No edit summary current
- 23:2123:21, 9 December 2008 diff hist +487 Contravariant functor No edit summary current
- 23:1923:19, 9 December 2008 diff hist +245 N Template:TOCright New page: {| cellspacing="0" cellpadding="0" style="clear: {{{clear|right}}}; margin-bottom: .5em; float: right; padding: .5em 0 .8em 1.4em; background: none; width: {{{width|{{{1|auto}}}}}};" {{#if... current
- 23:1923:19, 9 December 2008 diff hist +13 Functor No edit summary
- 23:1823:18, 9 December 2008 diff hist +310 Functor No edit summary
- 23:1723:17, 9 December 2008 diff hist +1,184 N Contravariant functor New page: ==Definition== ===Definition in basic terms=== Suppose <math>\mathcal{C}, \mathcal{D}</math> are categories. A '''contravariant functor''' <math>\mathcal{F}:\mathcal{C} \to ...
- 02:0402:04, 9 December 2008 diff hist +268 N Cocomplete category New page: {{category property}} ==Definition== A '''cocomplete category''' is a category in which all small colimits exist. In particular, it admits coproducts and coequalizers. ==Rel... current
- 02:0302:03, 9 December 2008 diff hist +89 Complete category No edit summary current
- 02:0302:03, 9 December 2008 diff hist +210 N Complete category New page: {{category property}} ==Definition== A '''complete category''' is a category that admits all small limits. In particular, it admits all categorical products, direct limit...
- 02:0002:00, 9 December 2008 diff hist +136 Monoidal category No edit summary current
- 01:5601:56, 9 December 2008 diff hist +514 N Symmetric monoidal category New page: {{category plus additional structure}} ==Definition== A '''symmetric monoidal category''' is a monoidal category <math>(\mathcal{C}, \otimes)</math> equipped with a commutativity iso... current
- 01:5201:52, 9 December 2008 diff hist +541 N Monoidal category New page: {{category plus additional structure}} ==Definition== A '''monoidal category''' is a category <math>\mathcal{C}</math> equipped with an additional operation, called a monoidal operat...
- 01:3501:35, 9 December 2008 diff hist +297 N Template:Defs facts and survey articles New page: '''VIEW''': [[Special:SearchByProperty/Defining ingredient/{{PAGENAME}}|Definitions built on this]] <nowiki>|</nowiki> [[Special:SearchByProperty/Fact about/{{PAGENAME}}|Facts about this]]... current
- 01:3401:34, 9 December 2008 diff hist +600 N Template:Basicdef New page: <includeonly>{{TOCright}}</includeonly> {{quotation|''This article is about a basic definition in category theory. The article text may, however, contain more material. Rate its utility as... current
- 01:3201:32, 9 December 2008 diff hist +781 N Opposite category New page: {{basicdef}} ==Definition== Suppose <math>\mathcal{C}</math> is a category. The '''opposite category''' to <math>\mathcal{C}</math>, denoted <math>\mathcal{C}^{op}</math>, is defined as ... current
- 01:2901:29, 9 December 2008 diff hist +22 N Template:Fillin New page: ''Fill this in later'' current
- 01:2901:29, 9 December 2008 diff hist +782 N Adjoint functors New page: ==Definition== Suppose <math>\mathcal{C}</math> and <math>\mathcal{D}</math> are categories. Suppose <math>\mathcal{F}:\mathcal{C} \to \mathcal{D}</math> and <math>\mathcal{G... current
- 01:2401:24, 9 December 2008 diff hist +171 N Zero object New page: ==Definition== An object in a category is termed a '''zero object''' if it is both an defining ingredient::initial object and a defining ingredient::final object.
- 01:2401:24, 9 December 2008 diff hist +263 Categorical product No edit summary current
- 01:2101:21, 9 December 2008 diff hist +89 Category No edit summary
- 01:2101:21, 9 December 2008 diff hist +601 N Categorical product New page: ==Definition== Suppose <math>\mathcal{C}</math> is a category and <math>A_1,A_2 \in \operatorname{Ob}\mathcal{C}</math>. A '''categorical product''', or simply '''product''', of <math>A_1...
- 01:1801:18, 9 December 2008 diff hist +33 N Product Redirecting to Categorical product current
- 01:1701:17, 9 December 2008 diff hist +545 N Final object New page: {{basicdef}} ==Definition== ===Definition with symbols=== An object <math>A</math> in a category <math>\mathcal{C}</math> is termed a '''final object''' if for every object <math>B ... current
- 01:1501:15, 9 December 2008 diff hist +268 Equivalence of categories No edit summary current
- 01:1401:14, 9 December 2008 diff hist +337 N Equivalence of categories New page: {{functor property}} ==Definition== ===Symbol-free definition=== An '''equivalence of categories]] is a functor between two categories that satisfies the following thre...
- 01:1201:12, 9 December 2008 diff hist +555 N Essentially surjective functor New page: {{basicdef}} {{functor property}} ==Definition== ===Symbol-free definition=== A functor is termed '''essentially surjective''' if every object in the target category is isomorph... current
- 01:0801:08, 9 December 2008 diff hist +592 N Initial object New page: {{basicdef}} ==Definition== Suppose <math>\mathcal{C}</math> is a category. An '''initial object''' in <math>\mathcal{C}</math> is an object <math>A \in \operatorname{Ob}\mathcal{C}</mat...
- 00:5800:58, 9 December 2008 diff hist +730 N Natural transformation New page: {{basicdef}} ==Definition== Suppose <math>\mathcal{C},\mathcal{D}</math> are categories, and <math>\mathcal{F}:\mathcal{C} \to \mathcal{D}</math> and <math>\mathcal{G}:\math... current
- 00:5300:53, 9 December 2008 diff hist +551 N Epimorphism New page: {{morphism property}} ==Definition== Suppose <math>\mathcal{C}</math> is a category, <math>A,B \in \operatorname{Ob}\mathcal{C}</math>, and <math>f \in \mathcal{C}(A,B)</math>. <math>f</... current
- 00:5000:50, 9 December 2008 diff hist +621 N Monomorphism New page: ==Definition== ===Definition with symbols=== Suppose <math>\mathcal{C}</math> is a category, <math>A,B \in \operatorname{Ob}\mathcal{C}</math>, and <math>f \in \mathcal{C}(A,B)</math... current
- 00:4600:46, 9 December 2008 diff hist +59 Template:Category property No edit summary
- 00:4500:45, 9 December 2008 diff hist 0 Template:Functor property No edit summary current
- 00:4500:45, 9 December 2008 diff hist +58 Template:Functor property No edit summary
- 00:4500:45, 9 December 2008 diff hist +255 N Template:Category plus additional structure New page: {{quotation|''This article defines a notion of a category along with some additional structure.''<br>View other such notions}}<include... current
- 00:4400:44, 9 December 2008 diff hist 0 Concrete category No edit summary current
- 00:4300:43, 9 December 2008 diff hist +324 N Concrete category New page: {{category with additional structure}} ==Definition== A '''concrete category''' is the data of a defining ingredient::category along with a defining ingredient::faithful functor ...
- 00:4100:41, 9 December 2008 diff hist +680 N Full functor New page: {{functor property}} ==Definition== ===Symbol-free definition=== A '''full functor''' is a functor such that the induced mapping on the collection of morphisms between any two objec... current
- 00:3800:38, 9 December 2008 diff hist +213 N MediaWiki:Sidebar New page: * SEARCH * navigation ** mainpage|mainpage-description ** portal-url|portal ** currentevents-url|currentevents ** recentchanges-url|recentchanges ** randompage-url|randompage ** helppage|h...