category theory, a branch of mathematics, a monad is a triple ( T , η , μ ) {\displaystyle (T,\eta ,\mu )} consisting of a functor T from a category to...
31 KB (4,489 words) - 19:57, 5 July 2025
In category theory and its applications to other branches of mathematics, kernels are a generalization of the kernels of group homomorphisms, the kernels...
7 KB (950 words) - 04:45, 20 May 2025
In algebraic K-theory, the K-theory of a category C (usually equipped with some kind of additional data) is a sequence of abelian groups Ki(C) associated...
12 KB (1,664 words) - 13:39, 1 March 2025
the theory of categories concerns itself with the categories of being: the highest genera or kinds of entities. To investigate the categories of being...
34 KB (4,649 words) - 22:33, 19 June 2025
Algebraic K-theory is a subject area in mathematics with connections to geometry, topology, ring theory, and number theory. Geometric, algebraic, and arithmetic...
77 KB (10,647 words) - 03:27, 4 May 2025
In mathematics, higher category theory is the part of category theory at a higher order, which means that some equalities are replaced by explicit arrows...
9 KB (1,016 words) - 14:35, 30 April 2025
In category theory, a branch of mathematics, a section is a right inverse of some morphism. Dually, a retraction is a left inverse of some morphism. In...
6 KB (794 words) - 07:10, 3 July 2025
In category theory, a discipline within mathematics, the nerve N(C) of a small category C is a simplicial set constructed from the objects and morphisms...
10 KB (1,489 words) - 10:45, 27 May 2025
K-theory is, roughly speaking, the study of a ring generated by vector bundles over a topological space or scheme. In algebraic topology, it is a cohomology...
27 KB (4,403 words) - 06:31, 11 May 2025
In category theory, a branch of mathematics, a pullback (also called a fiber product, fibre product, fibered product or Cartesian square) is the limit...
16 KB (2,061 words) - 08:26, 24 June 2025
In category theory, a branch of mathematics, a pushout (also called a fibered coproduct or fibered sum or cocartesian square or amalgamated sum) is the...
13 KB (1,984 words) - 23:29, 23 June 2025
category of sets, whose objects are sets and whose arrows are functions. Category theory is a branch of mathematics that seeks to generalize all of mathematics...
21 KB (2,525 words) - 18:54, 19 March 2025
In category theory, a branch of mathematics, a monoid (or monoid object, or internal monoid, or algebra) (M, μ, η) in a monoidal category (C, ⊗, I) is...
5 KB (511 words) - 22:41, 17 March 2025
equivariant algebraic K-theory is an algebraic K-theory associated to the category Coh G ( X ) {\displaystyle \operatorname {Coh} ^{G}(X)} of equivariant coherent...
5 KB (786 words) - 07:58, 13 August 2023
In stable homotopy theory, a branch of mathematics, Morava K-theory is one of a collection of cohomology theories introduced in algebraic topology by Jack...
3 KB (406 words) - 18:26, 29 March 2024
Spectrum (topology) (redirect from Stable homotopy category)
cohomology theory in degree k {\displaystyle k} on a space X {\displaystyle X} is equivalent to computing the homotopy classes of maps to the space E k {\displaystyle...
22 KB (3,449 words) - 17:37, 16 May 2025
In algebra, given a ring R, the category of left modules over R is the category whose objects are all left modules over R and whose morphisms are all...
4 KB (484 words) - 08:11, 19 June 2025
specifically category theory, a quasi-category (also called quasicategory, weak Kan complex, inner Kan complex, infinity category, ∞-category, Boardman complex...
22 KB (3,351 words) - 12:35, 11 June 2025
set as a skeleton. There many examples of skeletonization of fusion categories and related structures. Glossary of category theory Thin category Adámek...
4 KB (471 words) - 17:50, 1 March 2025
This is a glossary of properties and concepts in category theory in mathematics. (see also Outline of category theory.) Notes on foundations: In many...
78 KB (11,821 words) - 20:01, 5 July 2025
category D(A) of an abelian category A is a construction of homological algebra introduced to refine and in a certain sense to simplify the theory of...
29 KB (4,514 words) - 22:32, 28 May 2025
In mathematics, particularly in homotopy theory, a model category is a category with distinguished classes of morphisms ('arrows') called 'weak equivalences'...
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Functor (redirect from Functor (category theory))
In mathematics, specifically category theory, a functor is a mapping between categories. Functors were first considered in algebraic topology, where algebraic...
24 KB (3,550 words) - 22:28, 25 April 2025
Natural transformation (redirect from Natural (category theory))
In category theory, a branch of mathematics, a natural transformation provides a way of transforming one functor into another while respecting the internal...
35 KB (5,962 words) - 07:43, 5 June 2025
operator K-theory is a noncommutative analogue of topological K-theory for Banach algebras with most applications used for C*-algebras. Operator K-theory resembles...
4 KB (526 words) - 18:30, 8 November 2022
In category theory, a span, roof or correspondence is a generalization of the notion of relation between two objects of a category. When the category has...
4 KB (611 words) - 18:56, 29 January 2025
Adjoint functors (redirect from Unit (category theory))
specifically category theory, adjunction is a relationship that two functors may exhibit, intuitively corresponding to a weak form of equivalence between...
64 KB (10,260 words) - 08:58, 28 May 2025
Coproduct (redirect from Coproduct (category theory))
In category theory, the coproduct, or categorical sum, is a construction which includes as examples the disjoint union of sets and of topological spaces...
12 KB (2,130 words) - 16:31, 3 May 2025
mathematics, topological K-theory is a branch of algebraic topology. It was founded to study vector bundles on topological spaces, by means of ideas now recognised...
9 KB (1,349 words) - 19:33, 7 January 2025
especially category theory, an (∞, n)-category is a generalization of an ∞-category, where each k-morphism is invertible for k > n {\displaystyle k>n} . Thus...
876 bytes (70 words) - 11:21, 7 April 2025