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- ...[Taylor series]] of a [[smooth function]], hence the term "''calculus'' of functors". ...difficult to analyze directly, so the idea is to replace them with simpler functors which are sufficiently good approximations for certain purposes. ...7 KB (1,095 words) - 07:55, 4 March 2024
- ...nt functors''' are criteria for the existence of a left or right [[adjoint functors|adjoint]] of a given [[functor]]. ...reyd|2003|loc=Chapter 3. (pp.84–)}}</ref> an Introduction to the Theory of Functors'': ...6 KB (882 words) - 17:31, 16 August 2024
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- ...lex]]. It can be used to construct [[#Hyper-derived functors|hyper-derived functors]]. It is named in honor of [[Henri Cartan]] and [[Samuel Eilenberg]]. === Hyper-derived functors === ...3 KB (430 words) - 01:39, 16 December 2023
- ...|Grothendieck 1957]]</ref> In particular, derived functors are universal δ-functors. ===Morphisms of δ-functors=== ...4 KB (634 words) - 01:58, 17 October 2022
- ...rnal=Applied Categorical Structures|date=March 2014|title=On normal tensor functors and coset decompositions for fusion categories|first1=A.|last1=Bruguières|f [[Category:Functors]] ...901 bytes (143 words) - 04:03, 6 February 2025
- ...tegories]], a lax natural transformation is a kind of morphism between [[2-functors]]. ...'C'' and ''D'' be 2-categories, and let <math>F,G\colon C\to D</math> be 2-functors. A lax natural transformation <math>\alpha\colon F\to G</math> between them ...886 bytes (143 words) - 08:47, 2 January 2025
- *Charles E. Watts, Intrinsic characterizations of some additive functors, Proc. Amer. Math. Soc. 11, 1960, 5–8. *Samuel Eilenberg, Abstract description of some basic functors, J. Indian Math. Soc. (N.S.) 24, 1960, 231–234 (1961). ...1 KB (160 words) - 14:51, 6 December 2024
- ...s of vector spaces. Smooth functors may therefore be uniquely extended to functors defined on [[vector bundle]]s. ...Kriegl|Michor|1997|p=290}}. {{harvnb|Lee|2002}}, pp.122–23 defines smooth functors over a different category, whose morphisms are [[linear isomorphism]]s rath ...3 KB (475 words) - 20:12, 4 March 2024
- ...nserter category''' is a variation of the [[comma category]] where the two functors are required to have the same domain category. If ''C'' and ''D'' are two categories and ''F'' and ''G'' are two functors from ''C'' to ''D'', the inserter category Ins(''F'', ''G'') is the ca ...2 KB (261 words) - 09:34, 21 November 2023
- ...the [[exterior power]]s <math>V \mapsto \wedge^n(V)</math> are polynomial functors from <math>\mathcal{V}</math> to <math>\mathcal{V}</math>; these two are al ...ulus of functors]]). In particular, the category of homogeneous polynomial functors of degree ''n'' is equivalent to the [[category of representations|category ...3 KB (419 words) - 20:09, 4 March 2024
- ...l]].<ref>{{Cite journal |last=Dugger |first=Daniel |date=2022 |title=GYSIN FUNCTORS, CORRESPONDENCES, AND THE GROTHENDIECK-WITT CATEGORY |url=http://www.tac.mt ==Mackey functors== ...3 KB (497 words) - 08:32, 5 March 2024
- {{Functors}} ...1 KB (180 words) - 08:41, 5 March 2024
- ...[Taylor series]] of a [[smooth function]], hence the term "''calculus'' of functors". ...difficult to analyze directly, so the idea is to replace them with simpler functors which are sufficiently good approximations for certain purposes. ...7 KB (1,095 words) - 07:55, 4 March 2024
- If we apply this context to [[category of functors|functor categories]], and observe natural transformations <math>\boldsymbol The functors are also mapped accordingly as such: ...4 KB (531 words) - 07:27, 3 March 2025
- *<math>\varprojlim{}^1</math>, the first [[Inverse limit#Derived functors of the inverse limit|derived functor of the inverse limit]] ...309 bytes (42 words) - 16:56, 13 July 2024
- ...ed after [[Americans|American]] [[mathematician]] [[George Mackey]], these functors were first introduced by [[Germans|German]] mathematician [[Andreas Dress]] ...mathcal{C}</math>.<ref name="barwick">Barwick, C. (2017). "Spectral Mackey functors and equivariant algebraic K-theory (I)". ''Advances in Mathematics'', 304:6 ...4 KB (647 words) - 07:52, 6 January 2025
- {{Short description|Generalization of functors}} ...1 KB (245 words) - 17:41, 14 January 2022
- ...ctor <math>i\colon\mathcal{B}\rightarrow\mathcal{A}</math> has a [[adjoint functors|left adjoint]]. If this left adjoint of <math>i</math> also preserves ...mathcal{A}/\mathcal{C}\rightarrow\mathcal{A}</math> is [[full and faithful functors|fully faithful]] and induces an [[equivalence of categories|equivalence]] b ...2 KB (289 words) - 04:40, 28 August 2023
- ...e of this notion stems from the fact that kernels of [[exact functor|exact functors]] between abelian categories are Serre subcategories, and that one can buil [[Adjoint functors|right adjoint]] ...4 KB (545 words) - 15:02, 8 March 2023
- ...ref>{{cite journal |last1=Day |first1=Brian |title=On closed categories of functors |journal=Reports of the Midwest Category Seminar IV, Lecture Notes in Mathe ...a tensor product for a [[monoidal category]] structure on the category of functors <math>[\mathbf{C},V]</math> over some [[monoidal category]] <math>V</math>. ...4 KB (599 words) - 20:27, 28 January 2025
- ...oup generated by ''GX'', the generators of some group ''X''; see [[Adjoint functors#Free groups]] ...571 bytes (80 words) - 00:43, 11 August 2023
- ...refer to several loosely related [[functor|functors]] that generalise the functors taking a [[covering space]] <math>\pi\colon X\rightarrow S</math> to the '' ...a point <math>a</math> in <math>X</math> is equivalent to defining adjoint functors<blockquote><math>a^*:\mathfrak{T}(X)\leftrightarrows \mathfrak{Set}:a_*</ma ...6 KB (901 words) - 08:55, 13 December 2024