10 articles
2-category
A 2-category is a category-like structure with objects, 1-morphisms, and 2-morphisms between parallel morphisms; its weak form is the bicategory, introduced by Jean Bénabou in 1968.
Bicategory
A bicategory is a weak 2-category in which composition of morphisms is associative and has identities only up to invertible 2-morphisms, introduced by Jean Bénabou in 1967.
Category (mathematics)
In mathematics, a category is a structure consisting of objects together with morphisms between them, with identity morphisms and associative composition, introduced by Eilenberg and Mac Lane in 1945.
Category theory
Category theory is a branch of abstract algebra that studies mathematical structures through morphisms between objects. Eilenberg and Mac Lane introduced it in the 1940s.
Coproduct
A coproduct is a category-theoretic construction that combines objects by mapping into the result, dual to the product and realized as disjoint unions, free products, and direct sums.
Enriched category
An enriched category is a category-like structure whose hom-sets are replaced by objects of a monoidal base category, yielding ordinary categories, metric spaces, and 2-categories as instances.
Groupoid
A groupoid is a small category in which every morphism is an isomorphism, equivalently a set with a partial multiplication, introduced by Heinrich Brandt in 1926.
Kleisli category
A Kleisli category is a category built from a monad, keeping the base category's objects and taking morphisms X to Y to be morphisms X to T(Y).
Morphism
A morphism is an abstract arrow from one object of a category to another, with composition and identities, defined without reference to functions or sets.
Universal property
A universal property, also called a universal mapping property, defines a mathematical object by unique morphisms from every object of its category rather than by internal construction.