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267 B (44 words) - 09:35, 19 February 2016
- ...by arrows, where arrows compose'''. In fact that is the definition of a [[category]], a thing with objects and arrows, where the arrows compose. The most familiar category to the reader will be [[SET (category)|{{M|\mathrm{SET} }}]]2 KB (311 words) - 11:46, 19 February 2016
- For a pair of [[object|objects]] {{M|A}} and {{M|B}} in a [[category]] {{M|\mathscr{C} }} we define{{rAITCTHS2010}}: | ''({{AKA}}: [[cone (category theory)|cone]])''992 B (149 words) - 23:00, 28 February 2016
- ...the definitions for [[Cone (category theory)|cone]] and [[Cocone (category theory)|cocone]] are very similar and contrast each other well, see the page [[con Given two [[object (category theory)|objects]] {{M|A}}, {{M|B}} in a [[category]] {{M|\mathscr{C} }}, a ''cone''{{rAITCTHS2010}} is:1 KB (197 words) - 22:27, 28 February 2016
- ...the definitions for [[Cone (category theory)|cone]] and [[Cocone (category theory)|cocone]] are very similar and contrast each other well, see the page [[con Given two [[object (category theory)|objects]] {{M|A}}, {{M|B}} in a [[category]] {{M|\mathscr{C} }}, a ''cocone''{{rAITCTHS2010}} is:1 KB (182 words) - 22:28, 28 February 2016
- ...fleshing out with things like notation, compared to [[Coproduct (category theory)|coproduct]] and such}} ...mpared]] for a definition written in parallel with the [[product (category theory)|product]] definition. This demonstrates how close the concepts are.1 KB (192 words) - 19:46, 1 March 2016
- ...fleshing out with things like notation, compared to [[Coproduct (category theory)|coproduct]] and such}} ...mpared]] for a definition written in parallel with a [[coproduct (category theory)|coproduct]] definition. This demonstrates how close the concepts are.1 KB (192 words) - 23:32, 29 February 2016
- ...athop{\longrightarrow}^fB}} and {{M|B\mathop{\longrightarrow}^g A}} in a [[category]] {{M|\mathscr{C} }}, we say that {{M|f}} and {{M|g}} are ''isomorphisms''{ * [[Types of category arrows]]753 B (117 words) - 14:19, 13 March 2016
- #REDIRECT [[Coproduct (category theory)]] {{Definition|Category Theory}}72 B (7 words) - 20:12, 19 October 2016
- : This page shows {{link|Initial|category theory}} and {{link|Final|category theory}} side by side, for more details on each see their respective pages. Let {{M|\mathcal{C} }} be a [[category]] and let {{M|S\in\text{Ob}(\mathcal{C})}}, then we say {{M|S}} is:704 B (106 words) - 20:25, 15 November 2016
- : See [[initial and final compared (category theory)]] for this definition and its dual side by side ...y]] and let {{M|S\in\text{Ob}(\mathcal{C})}} be any {{link|object|category theory}} of {{M|\mathcal{C} }}. Then {{M|S}} is ''initial'' in {{M|\mathcal{C} }}817 B (122 words) - 20:30, 15 November 2016
- : See [[initial and final compared (category theory)]] for this definition and its dual side by side ...y]] and let {{M|S\in\text{Ob}(\mathcal{C})}} be any {{link|object|category theory}} of {{M|\mathcal{C} }}. Then {{M|S}} is ''final'' (or ''terminal''{{rAITCT806 B (120 words) - 20:32, 15 November 2016
- {{Definition|Category Theory}}53 B (5 words) - 15:10, 15 December 2017
Page text matches
- * Category * The category [[:Category:First-year friendly]] contains {{PAGESINCATEGORY:First-year friendly|pages}7 KB (999 words) - 16:51, 11 May 2020
- : '''Note: ''' not to be confused with [[Homomorphism]] which is a [[Category Theory (subject)|categorical]] construct. ...isn't'' {{M|\simeq}} (which is typically used for [[isomorphism (category theory)|isomorphic spaces]]) as that notation is used almost universally for [[hom5 KB (731 words) - 22:58, 22 February 2017
- ...rjection/injection/[[bijection]] to be seen through the lens of [[Category Theory]]. [[User:Alec|Alec]] ([[User talk:Alec|talk]]) 21:50, 8 May 2018 (UTC) {{Definition|Set Theory}}3 KB (463 words) - 21:50, 8 May 2018
- * [[Homomorphism (category theory)]] - which all the following are instances of ...omomorphism types listed here are examples of morphism in their respective category.4 KB (532 words) - 22:04, 19 October 2016
- {{Definition|Set Theory}} [[Category:Exemplary pages]]4 KB (659 words) - 13:01, 19 February 2016
- ...Only "major" results are shown, they are covered in the motivation for set theory page, and "D" denotes "definition" - which is something that is natural to | [[Motivation for set theory axioms#The empty set is unique|The empty set is unique]] can now be proved,3 KB (619 words) - 10:25, 11 March 2015
- This will follow the same format as the start of the [[Set theory axioms|set theory axioms]] page [[Category:Set Theory]]3 KB (584 words) - 23:03, 28 February 2015
- * Measure Theory * Measure Theory9 KB (1,490 words) - 06:13, 1 January 2017
- ...nce {{M|1=(A_i)_{i=1}^\infty}} is a function<ref>p46 - Introduction To Set Theory, third edition, Jech and Hrbacek</ref><ref name="Analysis">p11 - Analysis - {{Definition|Set Theory|Real Analysis|Functional Analysis}}2 KB (419 words) - 18:12, 13 March 2016
- {{Definition|Abstract Algebra|Group Theory}} {{Theorem Of|Abstract Algebra|Group Theory}}7 KB (1,332 words) - 07:17, 16 October 2016
- [[Category:Measure Theory]]4 KB (733 words) - 01:41, 28 March 2015
- * Measure Theory [[Category:Subjects]]409 B (62 words) - 15:49, 13 March 2015
- * [[:Category:Types of rings|Category for various types of rings]] {{Definition|Abstract Algebra|Ring Theory}}7 KB (1,248 words) - 05:02, 16 October 2016
- {{Ring theory navbox}} {{Definition|Abstract Algebra|Ring Theory}}2 KB (327 words) - 11:09, 20 February 2016
- | {{M|\backslash}}-closed<ref name="PTACC">Probability Theory - A comprehensive course - Second Edition - Achim Klenke</ref> [[Category:Index]]2 KB (360 words) - 20:43, 15 June 2015
- * [[Integral (measure theory)]] '''DONE''' [[User:Alec|Alec]] ([[User talk:Alec|talk]]) 02:01, 19 March * [[Integral of a simple function (measure theory)]] '''DONE''' [[User:Alec|Alec]] ([[User talk:Alec|talk]]) 02:01, 19 March5 KB (645 words) - 11:40, 21 August 2016
- [[Category:Index]] {{Definition|Measure Theory}}575 B (72 words) - 14:01, 18 March 2016
- {{Definition|Measure Theory}} [[Category:Exemplary pages]]1 KB (184 words) - 01:54, 19 March 2016
- [[Category:Index]] {{Definition|Abstract Algebra|Set Theory|Measure Theory}}1 KB (165 words) - 02:07, 3 August 2015
- ...">Conventionally, {{M|\mathcal{J} }} denotes the open sets, but in measure theory this seems to denote the sets of half-open-half-closed rectangles, and it i {{Definition|Measure Theory}}5 KB (854 words) - 09:25, 6 August 2015
- {{Definition|Measure Theory}} [[Category:Subset system]]960 B (158 words) - 15:43, 28 August 2015
- {{Definition|Set Theory}} {{Theorem Of|Set Theory}}1 KB (237 words) - 00:48, 21 March 2016
- {{Definition|Abstract Algebra|Ring Theory}}[[Category:Types of rings]]951 B (151 words) - 21:29, 19 April 2016
- A '''Category {{M|C}}''' consists of 3 things<ref name="EOAT">Elements of Algebraic Topol {{Definition|Category Theory}}2 KB (347 words) - 00:36, 27 September 2015
- ...conflicts or ambiguities I am trying to resolve|border=FF0000|bg=FFAD88}}[[Category:Todo]] [[Category:Index]]3 KB (632 words) - 20:32, 16 October 2015
- {{Definition|Manifolds|Functional Analysis|Real Analysis|Measure Theory}} [[Category:Examples of algebras]]2 KB (259 words) - 23:41, 21 October 2015
- {{Order theory navbox|plain}} [[Category:Order Theory]]3 KB (454 words) - 07:40, 11 April 2016
- {{Definition|Category Theory}}409 B (42 words) - 14:59, 2 February 2016
- * 3 objects, {{M|X}}, {{M|Y}} and {{M|Z}} in a [[category]] {{M|\mathscr{C} }} * a (covariant) functor from {{M|\mathscr{C} }} to another category, {{M|\mathscr{D} }}1 KB (205 words) - 16:27, 2 February 2016
- A ''covariant functor'', {{M|T:C\leadsto D}} (for [[category|categories]] {{M|C}} and {{M|D}}) is a pair of [[mapping|mappings]]{{rAIRMA {{Definition|Category Theory}}2 KB (253 words) - 15:47, 2 February 2016
- {{Definition|Category Theory}}157 B (15 words) - 16:30, 2 February 2016
- A ''covariant functor'', {{M|S:C\leadsto D}} (for [[category|categories]] {{M|C}} and {{M|D}}) is a pair of [[mapping|mappings]]{{rAIRMA {{Definition|Category Theory}}2 KB (263 words) - 16:53, 2 February 2016
- A ''bimorphism'' is a [[morphism]] or [[arrow]] in a [[category]] {{M|\mathscr{C} }}{{rAITCTHS2010}}: * both [[monic (category theory)|monic]] and [[epic (category theory)|epic]]577 B (82 words) - 14:23, 13 March 2016
- ==Diagram showing how terms for arrows in a category relate== [[Category:Diagrams showing how things relate]]738 B (101 words) - 14:50, 6 February 2016
- ...to another) between those sets as the [[arrows of a category|arrows of the category]]{{rAITCTHS2010}}. ...T} }} category is {{AKA}} {{M|\mathrm{SETS} }} (and the page <code>[[SETS (category)]]</code> redirects here)1 KB (168 words) - 10:05, 19 February 2016
- ...by arrows, where arrows compose'''. In fact that is the definition of a [[category]], a thing with objects and arrows, where the arrows compose. The most familiar category to the reader will be [[SET (category)|{{M|\mathrm{SET} }}]]2 KB (311 words) - 11:46, 19 February 2016
- #REDIRECT [[SET (category)]] {{Definition|Category Theory}}124 B (13 words) - 10:01, 19 February 2016
- ...wo huge subsubjects (?) if you will, [[Group Theory (subject)]] and [[Ring Theory (subject)]]. It also arguably has [[Linear Algebra (subject)]] too (via [[V ...e will end in (subject) and be in the [[:Category:Subjects]] and in the [[:Category:Mathematical subjects]]3 KB (469 words) - 11:31, 19 February 2016
- # Created [[Category Theory (subject)]] and the project page for subject refactoring. [[User:Alec|Alec] [[Category:Site project logs]]277 B (33 words) - 11:24, 19 February 2016
- * [[Site projects:Split set theory into elementary set theory]] ====Category Theory====868 B (93 words) - 12:15, 9 April 2016
- # The [[Template:Category theory navbox|Category theory navbox]] focuses too much on arrows and types of arrows. The diagram might [[Category:Site project tasks]]328 B (44 words) - 11:43, 19 February 2016
- ** [[Group Theory (subject)|Group Theory]] (see Group Theory for branches) ** [[Order Theory (subject)|Order Theory]] (see Order Theory for branches)2 KB (265 words) - 14:53, 26 February 2016
- {{Requires references|I know Introduction to Category Theory has the definition, Analysis (Maurin) might too!}} {{Definition|Set Theory|Order Theory|Abstract Algebra}}421 B (60 words) - 21:24, 19 April 2016
- * [[:Category:Abstract Algebra]] ({{PAGESINCATEGORY:Abstract Algebra|pages}} pages) - all * [[:Category:Abstract Algebra Definitions]] ({{PAGESINCATEGORY:Abstract Algebra Definiti2 KB (328 words) - 10:53, 20 February 2016
- ...from various kinds of orderings, called [[Lattice Theory (subject)|lattice theory]]. Some order theory is desired for parts of [[Analysis (subject)|analysis]], for this I recomme2 KB (217 words) - 15:26, 26 February 2016
- The ''{{M|\exists}}-functor'' is a [[covariant functor]] taking [[SET (category)|{{M|\mathrm{SET} }}]] {{M|\leadsto}} {{M|\mathrm{SET} }} defined as follow {{Category theory navbox|plain}}2 KB (317 words) - 17:51, 13 March 2016
- * [[Lower section]] - the [[dual (order theory)|dual]] concept to this ...functor, {{M|:}}[[PRE (category)|{{M|\mathrm{PRE} }}]]{{M|\leadsto}}[[TOP (category)|{{M|\mathrm{TOP} }}]] that uses this notion.1 KB (171 words) - 16:35, 20 February 2016
- ...nctor]] applied to an object in the [[PRE (category)|{{M|\mathrm{PRE} }}]] category.<br/> | The functor is {{M|\Uparrow:\mathrm{PRE}\leadsto}}[[TOP (category)|{{M|\mathrm{TOP} }}]], which takes [[preset|presets]] to [[topological spa2 KB (304 words) - 17:01, 20 February 2016
- ...opology {{M|\mathcal{J}_X}} on {{M|X}} and the arrows, or morphisms of the category are [[continuous function|continuous functions]]{{rAITCTHS2010}}. More expl {{Category theory navbox|plain}}971 B (139 words) - 20:10, 20 February 2016
- {{Group theory navbox|plain}} [[Category:Subjects]]170 B (23 words) - 14:43, 26 February 2016
- ...(subject)|Integration]] is a branch of [[Measure Theory (subject)|Measure Theory]] and VERY different to differentiation - at least in its roots, however as [[Category:Subjects]]691 B (94 words) - 14:56, 26 February 2016
- Number theory is a subject that studies the [[field]] of the [[integers]] The number theory project has:455 B (56 words) - 15:14, 26 February 2016
- Measure theory seeks to make the notion of measuring things formal. For example, given a r The measure theory project contains:832 B (121 words) - 15:24, 26 February 2016
- ...\rightarrow X}} and {{M|B\rightarrow X}} (which forms a [[cocone (category theory)|cocone]])) {{Definition|Category Theory|Linear Algebra}}495 B (77 words) - 21:56, 28 February 2016
- For a pair of [[object|objects]] {{M|A}} and {{M|B}} in a [[category]] {{M|\mathscr{C} }} we define{{rAITCTHS2010}}: | ''({{AKA}}: [[cone (category theory)|cone]])''992 B (149 words) - 23:00, 28 February 2016
- #REDIRECT [[Wedge (category theory)]] [[Category:Category Theory]]91 B (9 words) - 22:11, 28 February 2016
- ...a type of [[wedge (category theory)|wedge]] - see also [[cocone (category theory)|cocone]] {{Definition|Category Theory|Topology}}251 B (32 words) - 21:31, 20 April 2016
- ...the definitions for [[Cone (category theory)|cone]] and [[Cocone (category theory)|cocone]] are very similar and contrast each other well, see the page [[con Given two [[object (category theory)|objects]] {{M|A}}, {{M|B}} in a [[category]] {{M|\mathscr{C} }}, a ''cone''{{rAITCTHS2010}} is:1 KB (197 words) - 22:27, 28 February 2016
- ...the definitions for [[Cone (category theory)|cone]] and [[Cocone (category theory)|cocone]] are very similar and contrast each other well, see the page [[con Given two [[object (category theory)|objects]] {{M|A}}, {{M|B}} in a [[category]] {{M|\mathscr{C} }}, a ''cocone''{{rAITCTHS2010}} is:1 KB (182 words) - 22:28, 28 February 2016
- The pages [[Product (category theory))|product]] and [[Coproduct (category theory)|coproduct]] pages make it hard to see just how similar the two definitions Given a pair {{M|A}}, {{M|B}} of [[object|objects]] in a [[category]] {{M|\mathscr{C} }} a:2 KB (351 words) - 16:59, 1 March 2016
- ...fleshing out with things like notation, compared to [[Coproduct (category theory)|coproduct]] and such}} ...mpared]] for a definition written in parallel with the [[product (category theory)|product]] definition. This demonstrates how close the concepts are.1 KB (192 words) - 19:46, 1 March 2016
- ...fleshing out with things like notation, compared to [[Coproduct (category theory)|coproduct]] and such}} ...mpared]] for a definition written in parallel with a [[coproduct (category theory)|coproduct]] definition. This demonstrates how close the concepts are.1 KB (192 words) - 23:32, 29 February 2016
- * [[Product (category theory)]] - a categorical abstraction of the notion of product * [[Product (topology)]] - A [[categorical product]] in the [[TOP category]]489 B (67 words) - 00:03, 7 August 2016
- ...v\} }} and such where {{M|u,v:X\rightarrow\mathbb{R} }} as seen in measure theory. [[Category:Index]]360 B (61 words) - 07:49, 12 March 2016
- {{Stub page|grade=A|msg=Whenever working in a category we deal with morphisms, grade A because of urgency}} ...arrow'' is the name given for the directional links between objects of a [[category]], they are called (by definition) either arrows or morphism.514 B (73 words) - 22:10, 19 April 2016
- {{Definition|Category Theory}}54 B (5 words) - 12:13, 13 March 2016
- An [[arrow]], {{M|B\mathop{\longrightarrow}^mA}} in a [[category]] {{M|\mathscr{C} }} is ''monic'' if{{rAITCTHS2010}}: * [[Types of category arrows]]986 B (163 words) - 13:52, 13 March 2016
- An [[arrow]], {{M|A\mathop{\longrightarrow}^eB}} in a [[category]] {{M|\mathscr{C} }} is ''epic'' if{{rAITCTHS2010}}: * [[Types of category arrows]]987 B (163 words) - 13:59, 13 March 2016
- #REDIRECT [[Section (category theory)]] {{Definition|Category Theory}}71 B (7 words) - 14:00, 13 March 2016
- #REDIRECT [[Retraction (category theory)]] {{Definition|Category Theory}}74 B (7 words) - 14:02, 13 March 2016
- ...athop{\longrightarrow}^fB}} and {{M|B\mathop{\longrightarrow}^g A}} in a [[category]] {{M|\mathscr{C} }}, we say that {{M|f}} and {{M|g}} are ''isomorphisms''{ * [[Types of category arrows]]753 B (117 words) - 14:19, 13 March 2016
- ...l other isomorphism types are these [[arrow|arrows]] in their respective [[category|categories]] {{Definition|Category Theory}}229 B (27 words) - 14:22, 13 March 2016
- {{Definition|Category Theory}}54 B (5 words) - 18:04, 13 March 2016
- To make sure each page CURRENTLY in the Measure Theory category (as of 19th March 2016, 0035 GMT) are all up to a decent standard. A lot of {{:Site projects:Patrolling measure theory/Task list}}641 B (100 words) - 02:13, 19 March 2016
- ...thors to see what is what. Bogachev for example (author of [[Books:Measure Theory - Volume 1 - V. I. Bogachev]]) doesn't require that a measure even be posit # [[Books:Measure Theory - Volume 1 - V. I. Bogachev]]5 KB (771 words) - 03:06, 21 March 2016
- {{Definition|Set Theory}} [[Category:Set operations]]79 B (8 words) - 00:43, 21 March 2016
- {{Definition|Set Theory|Measure Theory}} [[Category:Set operations]]830 B (139 words) - 00:59, 21 March 2016
- {{Definition|Set Theory|Measure Theory}} [[Category:Set operations]]94 B (10 words) - 01:53, 21 March 2016
- {{Notes|Measure Theory}}[[Category:Finished notes]]2 KB (449 words) - 19:26, 24 May 2016
- Inline with the [[Notes:Measure theory plan]] page we will use the terms and symbols which may be found on the bot * A page (perhaps [[measure theory and sigma algebras notice]] will need to (have part of it) be transcluded o2 KB (309 words) - 15:31, 27 March 2016
- ...[[Algebra of sets|an algebra of sets]] (as would be encountered in measure theory) see [[Algebra (disambiguation)]] for all uses (See also the category: [[:Category:Examples of algebras|Examples of algebras]])2 KB (351 words) - 05:26, 1 January 2017
- ...alued]]'' [[countably additive set function]] defined on a [[ring (measure theory)|ring]]. Inline with the primary measure theory references{{rMTH}}{{rMIAMRLS}}{{rMT1VIB}} there are 3 steps to constructing2 KB (232 words) - 03:57, 30 March 2016
- [[Category:Infoboxes]] [[Category:Measure Theory]]427 B (68 words) - 18:43, 1 April 2016
- ...ires references|Find an order theory book, also I think that huge category theory PDF (Harold Simmons) has it}} {{Order theory navbox|plain}}1 KB (190 words) - 04:50, 9 April 2016
- {{Definition|Set Theory}}[[Category:Function Terminology]]575 B (89 words) - 20:02, 8 April 2016
- {{Definition|Set Theory}}[[Category:Function Terminology]]652 B (107 words) - 20:01, 8 April 2016
- ...y pages tagged as elementary set theory have no business in the set theory category. * Create an "elementary set theory" subject in the [[Site:Mathematical subject index]]739 B (114 words) - 12:21, 9 April 2016
- ! [[:Category:Refactoring grade A pages|A]] ! [[:Category:Refactoring grade B pages|B]]2 KB (425 words) - 02:21, 12 April 2016
- [[Category:Types of relation]] {{Definition|Set Theory}}94 B (11 words) - 20:05, 20 April 2016
- {{Definition|Set Theory}} [[Category:Types of relation]]95 B (11 words) - 20:06, 20 April 2016
- {{Definition|Set Theory}} [[Category:Types of relation]]94 B (11 words) - 20:07, 20 April 2016
- {{Definition|Topology|Homotopy Theory}} {{Homotopy theory navbox|plain}}4 KB (674 words) - 13:26, 15 September 2016
- Given a pair of groups, {{M|(A,*_A)}} and {{M|(B,*_B)}} in the [[category]] of [[groups]] we define the following: ===[[Product (category theory)|Product]]===4 KB (766 words) - 04:11, 3 July 2016
- #REDIRECT [[Product (category theory)]] {{Definition|Category Theory}}70 B (7 words) - 12:35, 7 July 2016
- #REDIRECT [[coproduct (category theory)]] {{Definition|Category Theory}}72 B (7 words) - 12:39, 7 July 2016
- {{Corollary Of|Group Theory|Abstract Algebra}} {{Group theory navbox|plain}}4 KB (727 words) - 04:53, 20 July 2016
- ...the [[category|categorical]] sense (of the [[GROUP|{{M|\mathrm{GROUP} }}]] category) {{Group theory navbox|plain}}568 B (93 words) - 11:28, 20 July 2016
- ...gory theory)]] - the coproducts below are instances of this in their own [[category]] ** [[Coproduct (topology)]] - a [[categorical coproduct]] in the [[TOP category]]577 B (74 words) - 13:22, 20 October 2016
- #REDIRECT [[Coproduct (category theory)]] {{Definition|Category Theory}}72 B (7 words) - 00:07, 7 August 2016
- #REDIRECT [[Product (category theory)]] {{Definition|Category Theory}}70 B (7 words) - 00:08, 7 August 2016
- ...r I am happy that this is a vector space. It's a class [[product (category theory)]]}}8 KB (1,463 words) - 14:35, 13 August 2016
- # Make it clear that is is [[:Category:Invented terminology|invented terminology]] and what the usual terms are : This page is a result of the [[Doctrine:Measure theory terminology]] document. It is not a well known term. [[mu*-measurable set|{2 KB (378 words) - 22:09, 20 August 2016
- :* {{Note|This comes from [[Books:An Introduction to Category Theory - Harold Simmons - 1st September 2010 edition]], along with most of the pag {{Definition|Set Theory|Elementary Set Theory}}2 KB (462 words) - 22:26, 23 August 2016
- ...ry|s}} are ''[[finite]]'' {{plural|set|s}} and whose {{link|arrow|category theory|s}}, {{M|\xymatrix{A \ar[r]^f & B} }} are {{plural|function|s}}{{rAITCTHS20 : '''Claim: ''' this is indeed a category<ref name="AITCTHS2010"/>.2 KB (275 words) - 12:29, 15 September 2016
- {{Definition|Elementary Set Theory}} {{Todo|Does this go in the relations category too? Yes...but what was it called again!?}}149 B (22 words) - 22:29, 18 September 2016
- ...The {{link|coproduct|category theory}} construction, in the ''[[SET]]'' [[category]] {{Definition|Set Theory|Elementary Set Theory|Topology}}552 B (86 words) - 23:29, 25 September 2016
- ...[sets]]. We denote their ''disjoint union'' or ''{{link|coproduct|category theory}}'' as {{M|1=\coprod_{\alpha\in I}X_\alpha}} and we define this to be: {{Set theory navbox|plain}}1 KB (210 words) - 20:21, 25 September 2016
- {{Todo|Link to category theory}}1 KB (166 words) - 11:00, 26 September 2016
- ...ectiveness) trivial, we do it anyway. That's why this page is marked as [[:Category:First-year friendly|first-year friendly]] {{Definition|Set Theory|Elementary Set Theory}}[[Category:First-year friendly]]4 KB (813 words) - 11:53, 26 September 2016
- A homeomorphism is an {{link|isomorphism|category theory}} in the [[TOP]] ''[[category]]'', as such it is an [[equivalence relation]] on the morphisms (which are883 B (132 words) - 11:52, 8 October 2016
- ...This may not be a [[homeomorphism]] (a topological [[isomorphism (category theory)|isomorphism]] however! That would require its inverse was also continuous<2 KB (264 words) - 22:32, 9 October 2016
- Which theorem of [[Group Theory (subject)|group theory]] does this resemble? ...ism (a homeomorphism is the term for a topological [[isomorphism (category theory)|isomorphism]]. Here are diagrams:3 KB (413 words) - 00:13, 12 October 2016
- {{Definition|Abstract Algebra|Ring Theory}}[[Category:ASN]]455 B (57 words) - 16:32, 19 October 2016
- {{Definition|Abstract Algebra|Ring Theory}}[[Category:ASN]]435 B (56 words) - 04:28, 16 October 2016
- {{Definition|Abstract Algebra|Ring Theory}}[[Category:ASN]]80 B (9 words) - 04:29, 16 October 2016
- {{Definition|Abstract Algebra|Ring Theory}}[[Category:ASN]]426 B (52 words) - 04:30, 16 October 2016
- ...]]. {{M|f}} is a ''ring homomorphism'' (or just ''[[homomorphism (category theory)|homomorphism]]'', or [[morphism]], if the context is clear) if{{rFOAANHM}} ** An instance of [[isomorphism (category theory)]] - see [[isomorphism]] for a disambiguation.972 B (171 words) - 04:50, 16 October 2016
- #REDIRECT [[Coproduct (category theory)]] {{Definition|Category Theory}}72 B (7 words) - 20:12, 19 October 2016
- * [[Direct product of modules]] - an instance of a {{link|product|category theory}} ...rnal direct sum of modules]] - an instance of a {{link|co-product|category theory}}1 KB (246 words) - 22:40, 19 October 2016
- * [[Direct sum of modules]] - instances of a {{link|co-product|category theory}} {{Definition|Abstract Algebra|Module Theory}}3 KB (431 words) - 22:19, 19 October 2016
- * {{link|Endomorphism|category theory}} - homomorphism of the form {{M|(:M\rightarrow M)}} - so from a module to * {{link|Monomorphism|category theory}} - any injective homomorphism<ref name="AAPAG"/>.3 KB (432 words) - 22:20, 19 October 2016
- * [[Coproduct (category theory)]] {{Definition|Abstract Algebra|Module Theory}}2 KB (278 words) - 14:05, 20 October 2016
- #REDIRECT [[Isomorphism (category theory)]] {{Definition|Category Theory}}130 B (14 words) - 14:59, 20 October 2016
- I really want like a [[Category Theory (subject)|categorical]] approach to the quotient group. Not "and look, if w1 KB (170 words) - 15:57, 26 October 2016
- {{Definition|Set Theory|Elementary Set Theory}}[[Category:Function Terminology]]112 B (12 words) - 21:04, 1 November 2016
- {{Definition|Elementary Set Theory|Set Theory}}[[Category:Function Terminology]]977 B (169 words) - 21:12, 1 November 2016
- {{Definition|Elementary Set Theory|Set Theory}}[[Category:Function Terminology]]112 B (12 words) - 21:12, 1 November 2016
- {{Definition|Elementary Set Theory|Set Theory}}[[Category:Function Terminology]]103 B (11 words) - 05:03, 3 November 2016
- {{Todo|Create a category and start collecting}} {{Definition|Set Theory|Abstract Algebra|Elementary Set Theory}}3 KB (478 words) - 18:58, 9 November 2016
- : This page shows {{link|Initial|category theory}} and {{link|Final|category theory}} side by side, for more details on each see their respective pages. Let {{M|\mathcal{C} }} be a [[category]] and let {{M|S\in\text{Ob}(\mathcal{C})}}, then we say {{M|S}} is:704 B (106 words) - 20:25, 15 November 2016
- : See [[initial and final compared (category theory)]] for this definition and its dual side by side ...y]] and let {{M|S\in\text{Ob}(\mathcal{C})}} be any {{link|object|category theory}} of {{M|\mathcal{C} }}. Then {{M|S}} is ''initial'' in {{M|\mathcal{C} }}817 B (122 words) - 20:30, 15 November 2016
- : See [[initial and final compared (category theory)]] for this definition and its dual side by side ...y]] and let {{M|S\in\text{Ob}(\mathcal{C})}} be any {{link|object|category theory}} of {{M|\mathcal{C} }}. Then {{M|S}} is ''final'' (or ''terminal''{{rAITCT806 B (120 words) - 20:32, 15 November 2016
- [[Category:Index]]{{Definition|Order Theory|Set Theory}}4 KB (656 words) - 18:45, 8 January 2017
- [[Category:Index]]{{Theorem Of|Elementary Set Theory|Set Theory}}497 B (85 words) - 14:46, 31 January 2017
- ...{M|A}} and {{M|C}} has the effect of creating a {{link|transposition|group theory}} between those letters<ref group="Note" name="TranspositionOwnInverse"/>, [[Category:Enigma Machine]][[Category:Cryptography]]5 KB (834 words) - 14:25, 15 December 2017
- ...lgebra, the {{plural|canonical projection|s}} of a {{link|product|category theory}} or a [[projector]] matrix.6 KB (1,051 words) - 07:44, 13 December 2017
- ...applied, these are taken in the context of [[Group Theory (subject)|Group Theory]] and represent elements from the [[permutation group]] {{M|S_{26} }}, {{M| [[Category:Enigma Machine]][[Category:Cryptography]]4 KB (696 words) - 15:24, 15 December 2017
- ...ub page|grade=D|msg=Needs references and such, to make it as nice as the [[category]] page}} ...et]] ([[subclass]] for certain kinds of category) of those in the "parent" category. Same as every other sub(object).358 B (55 words) - 14:59, 15 December 2017
- {{Definition|Elementary Set Theory|Set Theory|Abstract Algebra|Category Theory}}1 KB (235 words) - 15:06, 15 December 2017
- {{Definition|Category Theory}}53 B (5 words) - 15:10, 15 December 2017
- {{Definition|Set Theory|Elementary Set Theory|Category Theory}}89 B (10 words) - 15:35, 12 January 2018
- {{Stub page|grade=A**|msg=Needs to be linked to order theory stuff. Also: ...egorical product|characteristic projections]] of a {{link|product|category theory}}, and3 KB (473 words) - 07:53, 28 July 2018
