The following outline is provided as an overview of and guide to category theory, the area of study in mathematics that examines in an abstract way the properties of particular mathematical concepts, by formalising them as collections of objects and arrows (also called morphisms, although this term also has a specific, non category-theoretical sense), where these collections satisfy certain basic conditions. Many significant areas of mathematics can be formalised as categories, and the use of category theory allows many intricate and subtle mathematical results in these fields to be stated, and proved, in a much simpler way than without the use of categories.

Essence of category theory

Branches of category theory

Specific categories



Main article: Morphism


Main article: Functor


Main article: Limit (category theory)

Additive structure

Dagger categories

Main article: Dagger category

Monoidal categories

Main article: Monoidal category

Cartesian closed category


Main article: Structure (category theory)

Topoi, toposes

History of category theory

Persons influential in the field of category theory

Category theory scholars

See also