category
algebraic structure of objects and morphisms between objects, which can be associatively composed if the (co)domains agree
category of medial magmas
category in mathematics
closed category
category with an internal hom functor
fibered category
a “sheaf” of categories over a topological space (or, more generally, any category), where instead of equality we have natural equivalences in the definition of the sheaf axioms
filtered category
nonempty category such that for any two objects 𝑥, 𝑦 there exists a diagram 𝑥→𝑧←𝑦 and for every two parallel arrows 𝑓,𝑔: 𝑥→𝑦 there exists an ℎ: 𝑦→𝑧 such that ℎ∘𝑓=ℎ∘𝑔
subcategory
in mathematics, a category, whose objects and morphisms are inside a bigger category
model category
Mathematical category with weak equivalences, fibrations and cofibrations
complete category
category with all limits of (small) diagrams
category of relations
category of sets and relations
category of topological vector spaces
topological category
derived category
homotopy category of chain complexes in an abelian category with inverses to quasi-isomorphisms adjoined
allegory
in mathematics, a category that has some of the structure of the category of sets and binary relations between them
product category
product of two categories, in category theory
functor category
category containing functors with natural transformations as morphisms
regular category
kind of category that has similarities to both Abelian categories and to the category of sets
dagger category
category C equipped with an involutive functor †: Cᵒᵖ → C that is the identity on objects
groupoid
category where every morphism is invertible; generalization of a group
discrete category
category whose only arrows are identity arrows
opposite category
category constructed from another category C, whose objects are the same as those of C, whose morphisms from X to Y are the same as the morphisms in C from Y to X
locally small category
category whose morphisms between every two objects form a set
category of small categories
category whose objects are all small categories and whose morphisms are functors between categories
free category
category generated from a quiver by from freely concatenating arrows together, whenever the target of one arrow is the source of the next
simplex category
small category, whose objects are sets of natural numbers of the form {0,1,…,n}, and whose morphisms are nondecreasing functions