Outline of category theory

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The following outline is provided as an overview of and guide to category theory:

Category theory – 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[edit]

Main article: Category theory

Branches of category theory[edit]

Specific categories[edit]



Main article: morphism


Main article: Functor


Additive structure[edit]

Dagger categories[edit]

Main article: Dagger category

Monoidal categories[edit]

Main article: monoidal category

Cartesian closed category[edit]


Topoi, toposes[edit]

Main article: Topos

History of category theory[edit]

Main article: History of category theory

Persons influential in the field of category theory[edit]

Category theory scholars[edit]

See also[edit]


External links[edit]