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- ...one of its [[object (category theory)|objects]] <math>X</math> is itself a topos. Moreover, if there is a [[morphism]] <math>f : A \rightarrow B </math> in .../ A</math>, which is why any slice <math>\mathbf{E} / A </math> is also a topos. ...4 KB (700 words) - 09:43, 27 September 2022
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- ...t3=Spitters|first3=Bas|date=2009-10-01|title=A Topos for Algebraic Quantum Theory|journal=[[Communications in Mathematical Physics]]|language=en|volume=291|i ...ontext is not obvious. One can introduce the notion of a '''locally ringed topos''' by introducing a sort of geometric conditions of [[local rings]] (see SG ...5 KB (852 words) - 22:22, 14 January 2021
- ...one of its [[object (category theory)|objects]] <math>X</math> is itself a topos. Moreover, if there is a [[morphism]] <math>f : A \rightarrow B </math> in .../ A</math>, which is why any slice <math>\mathbf{E} / A </math> is also a topos. ...4 KB (700 words) - 09:43, 27 September 2022
- ...ary [[Topos#Elementary_topoi_(topoi_in_logic)|topos]], used to construct a topos of sheaves. A Lawvere–Tierney topology is also sometimes also called a '''l If ''E'' is a topos, then a topology on ''E'' is a morphism ''j'' from the [[subobject classifi ...4 KB (550 words) - 16:57, 3 February 2024
- '''Fiber functors''' in [[category theory]], [[topology]] and [[algebraic geometry]] refer to several loosely related ...alent to the category of sets, <math>\mathfrak{Set}</math>. If we have the topos of sheaves on a topological space <math>X</math>, denoted <math>\mathfrak{T ...6 KB (901 words) - 08:55, 13 December 2024
- ...ent category is taken to be the [[category of sets]] then one recovers the theory of small categories. In general, internal categories consist of a pair of o ...1</math> subject to coherence conditions expressing the axioms of category theory. See ...2 KB (356 words) - 14:53, 21 January 2021
- ...e mathematical idea of [[computability|effectivity]] within the [[category theory|category theoretical]] framework. The [[topos]] is based on the partial [[Combinatory logic|combinatory]] algebra given b ...9 KB (1,339 words) - 22:55, 6 August 2024
- ...Hausdorff space]]s. They can be used as a foundation for [[higher category theory]], where they can play the role of (<math>\infty</math>,1)-categories. An i *{{Citation | last1=Lurie | first1=Jacob | title=Higher topos theory | arxiv=math.CT/0608040 | publisher=[[Princeton University Press]] | series ...1 KB (160 words) - 15:18, 8 November 2024
- ...|derived]]" version of a fully faithful descent in the classical [[descent theory]]. This point is made precise by the below: the following are equivalent:<r The treatment in SGA uses a lot of [[topos theory]]. Conrad's notes gives a more down-to-earth exposition. ...1 KB (209 words) - 19:47, 6 July 2023
- ...t the topos of a point gives the special case of commutative rings, so the topos hypothesis can be ignored on a first reading. ...p</math> has the property <math>I^2 = (0)</math> is the zero [[ideal (ring theory)|ideal]]. ...11 KB (1,780 words) - 00:50, 28 October 2024
- ...,<ref>{{Cite journal |last=Raptis |first=George |date=2010 |title=Homotopy theory of posets |url=https://www.intlpress.com/site/pub/pages/journals/items/hha/ *Ch. 2 of Lurie's ''[[Higher Topos Theory]]''. ...2 KB (258 words) - 17:10, 19 February 2023
- ...lized to the case of sheaves of modules over a [[ringed space]], or ringed topos. In Grothendieck's duality theory of coherent sheaves on a projective scheme <math>i:X \hookrightarrow \mathb ...4 KB (670 words) - 21:33, 19 June 2023
- ...h <math>\infty</math> being the distance between two [[connectivity (graph theory)|unconnected]] vertices.{{sfnp|Koch|2020}} They can be used to show the ext In [[topology]], the [[topos]] of right [[semigroup action|actions]] on the extended natural numbers is ...4 KB (617 words) - 19:00, 28 January 2023
- ...singular algebraic varieties and [[cotangent complex]]es in [[deformation theory]] (cf. J. Francis), among the other applications. ...rsection number. (Currently this is hypothetical; the derived intersection theory has yet to be developed.) ...14 KB (2,044 words) - 17:44, 31 July 2024
- ...ategory]]. The study of such generalizations is known as [[higher category theory]]. ...ms have their analogues for quasi-categories. An elaborate treatise of the theory of quasi-categories has been expounded by {{harvs|txt|authorlink=Jacob Luri ...9 KB (1,248 words) - 03:16, 4 January 2025
- ...expressing many mathematical theories and has close connections to [[topos theory]]. A theory of first-order logic is geometric if it is can be axiomatised using only ax ...4 KB (622 words) - 07:17, 4 June 2024
- In [[mathematics]], a '''topos''' ({{IPAc-en|US|ˈ|t|ɒ|p|ɒ|s}}, {{IPAc-en|UK|ˈ|t|oʊ|p|oʊ|s|,_|ˈ|t|oʊ|p|ɒ|s} The mathematical field that studies topoi is called '''topos theory'''. ...32 KB (4,923 words) - 06:15, 25 February 2025
- ...Suppose ''X'' is a [[topological space]] which is the [[Pushout (category theory)|pushout]] of the diagram ...nd homotopy toposes |year=2010|url=http://www.math.uiuc.edu/~rezk/homotopy-topos-sketch.pdf|at= Prop. 8.16}}</ref> ...5 KB (690 words) - 05:20, 13 May 2023
- In [[intuitionistic type theory]] (ITT), a discipline within [[mathematical logic]], '''induction-induction ....1.6.4575|s2cid=18271311}}</ref> and limit constructions in category/topos theory. ...3 KB (451 words) - 01:25, 4 July 2024
- | known_for = [[Category theory]]<br/>[[Combinatorics]]<br/>[[Universal algebra]] ...olean valued set theory'', which introduced many students to [[topos|topos theory]].<ref name=ps>{{cite web|url= http://permalink.gmane.org/gmane.science.mat ...11 KB (1,317 words) - 19:10, 9 April 2024
- ...eadditive]] and is such that every [[idempotent]] has a [[kernel (category theory)|kernel]].<ref>Artin, 1972, p. 413.</ref> Recall that an idempotent [[morph ...= Séminaire de Géométrie Algébrique du Bois Marie - 1963-64 - Théorie des topos et cohomologie étale des schémas - (SGA 4) - vol. 1 (Lecture notes in mathe ...3 KB (494 words) - 22:41, 27 February 2024