Outline of category theory

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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





Additive structure

Dagger categories

Monoidal categories

Cartesian closed category


Topoi, toposes

History of category theory

Persons influential in the field of category theory

Category theory scholars

See also

Related Research Articles

Category theory Branch of mathematics

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Homological algebra area of mathematics

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This is a glossary of properties and concepts in category theory in mathematics.

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