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...

Category theory is a general theory of mathematical structures and their relations. It was introduced by Samuel Eilenberg and Saunders Mac Lane in the...

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 category theory, a branch of mathematics, a pushout (also called a fibered coproduct or fibered sum or cocartesian square or amalgamated sum) is the...

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 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...

by sectioning Section (category theory), a right inverse of some morphism Section (fiber bundle), in topology Part of a sheaf (mathematics) Section (group...

object. A simple example is the category of sets, whose objects are sets and whose arrows are functions. Category theory is a branch of mathematics that...

In category theory and its applications to mathematics, a normal monomorphism or conormal epimorphism is a particularly well-behaved type of morphism...

In category theory, a branch of mathematics, the image of a morphism is a generalization of the image of a function. Given a category C {\displaystyle...

In mathematics, a morphism is a concept of category theory that generalizes structure-preserving maps such as homomorphism between algebraic structures...

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...

a sheaf on a category with respect to some Grothendieck topology, have provided applications to mathematical logic and to number theory. In many mathematical...

In category theory, a branch of mathematics, the cone of a functor is an abstract notion used to define the limit of that functor. Cones make other appearances...

In mathematics, the Elementary Theory of the Category of Sets or ETCS is a set of axioms for set theory proposed by William Lawvere in 1964. Although it...

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

The theory of characteristic classes generalizes the idea of obstructions to our extensions. Section (category theory) Fibration Gauge theory (mathematics)...

In category theory, the concept of an element, or a point, generalizes the more usual set theoretic concept of an element of a set to an object of any...

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

general is in category theory. The algebraic objects to which representation theory applies can be viewed as particular kinds of categories, and the representations...

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

In category theory, a branch of mathematics, a sieve is a way of choosing arrows with a common codomain. It is a categorical analogue of a collection...

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

In mathematics, specifically category theory, a family of generators (or family of separators) of a category C {\displaystyle {\mathcal {C}}} is a collection...

abelian categories, and in group theory, where they are also known as sections, though this conflicts with a different meaning in category theory. So in...

In category theory, a branch of abstract mathematics, an equivalence of categories is a relation between two categories that establishes that these categories...

This is a timeline of category theory and related mathematics. Its scope ("related mathematics") is taken as: Categories of abstract algebraic structures...

In category theory, a category is Cartesian closed if, roughly speaking, any morphism defined on a product of two objects can be naturally identified...

In mathematics, especially in category theory and homotopy theory, a groupoid (less often Brandt groupoid or virtual group) generalises the notion of...

Fibred categories (or fibered categories) are abstract entities in mathematics used to provide a general framework for descent theory. They formalise the...