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...

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...

In category theory and its applications to other branches of mathematics, kernels are a generalization of the kernels of group homomorphisms, the kernels...

the theory of categories concerns itself with the categories of being: the highest genera or kinds of entities. To investigate the categories of being...

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...

Algebraic K-theory is a subject area in mathematics with connections to geometry, topology, ring theory, and number theory. Geometric, algebraic, and arithmetic...

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...

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...

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...

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...

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...

In category theory, a branch of mathematics, a pullback (also called a fiber product, fibre product, fibered product or Cartesian square) is the limit...

This is a glossary of properties and concepts in category theory in mathematics. (see also Outline of category theory.) Notes on foundations: In many...

equivariant algebraic K-theory is an algebraic K-theory associated to the category Coh G ⁡ ( X ) {\displaystyle \operatorname {Coh} ^{G}(X)} of equivariant coherent...

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...

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...

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...

specifically category theory, a quasi-category (also called quasicategory, weak Kan complex, inner Kan complex, infinity category, ∞-category, Boardman complex...

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...

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...

In mathematics, specifically category theory, a functor is a mapping between categories. Functors were first considered in algebraic topology, where algebraic...

In mathematics, particularly in homotopy theory, a model category is a category with distinguished classes of morphisms ('arrows') called 'weak equivalences'...

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...

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...

set as a skeleton. There many examples of skeletonization of fusion categories and related structures. Glossary of category theory Thin category Adámek...

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...

In category theory, a branch of mathematics, a natural transformation provides a way of transforming one functor into another while respecting the internal...

In category theory in mathematics, a 2-category is a category with "morphisms between morphisms", called 2-morphisms. A basic example is the category Cat...

specifically category theory, adjunction is a relationship that two functors may exhibit, intuitively corresponding to a weak form of equivalence between...

triangulated categories, an important example being the theory of sheaf cohomology. In the 1960s, a typical use of triangulated categories was to extend...