LIST OF CATEGORY THEORY TOPICS

This is a 'list of category theory topics', by Wikipedia page.

Contents

Specific categories

Objects

Limits

Additive structure

Topoi, toposes

Specific categories

★ Category of sets

★
★ Concrete category

★ Category of vector spaces

★
★ Category of graded vector spaces

★ Category of finite dimensional Hilbert spaces

★ Category of sets and relations

★ Category of topological spaces

★ Category of metric spaces

★ Category of preordered sets

★ Category of groups

★ Category of abelian groups

★ Category of commutative rings

★ Category of magmas

★ Category of medial magmas

Objects

★ Initial object

★ Terminal object

★ Zero object

★ Subobject

★ Group object

★ Magma object

★ Natural number object

★ Exponential object
==Morphisms==

★ Epimorphism

★ Monomorphism

★ Zero morphism

★ Normal morphism

★ Dual (category theory)

★ Groupoid

★ Image (category theory)

★ Coimage

★ Commutative diagram

★ Cartesian morphism

★ Slice category
==Functors==

★ Isomorphism of categories

★ Natural transformation

★ Equivalence of categories

★ Subcategory

★ Faithful functor

★ Full functor

★ Forgetful functor

★ Yoneda lemma

★ Representable functor

★ Functor category

★ Adjoint functors

★
★ Galois connection

★
★ Pontryagin duality

★
★ Affine scheme

★ Monad (category theory)

★ Comonad

★ Combinatorial species

★ Exact functor

★ Derived functor

★ Enriched functor

★ Kan extension of a functor

★ Hom functor

Limits

★ Limit (category theory)

★
★ Product (category theory)

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★ Equaliser (mathematics)

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★ Kernel (category theory)

★
★ Pullback (category theory), fiber product

★
★ Inverse limit

★
★
★ Pro-finite group

★ Colimit

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★ Coproduct

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★ Coequalizer

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★ Cokernel

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★ Pushout (category theory)

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★ Direct limit

★ Biproduct

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★ Direct sum

Additive structure

★ Preadditive category

★ Additive category

★ Pre-Abelian category

★ Abelian category

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★ Exact sequence

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★ Exact functor

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★ Snake lemma

★
★
★ Nine lemma

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★ Five lemma

★
★
★ Short five lemma

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★ Mitchell's embedding theorem

★ Injective cogenerator

★ Derived category

★ Triangulated category

★ Model category

★ 2-category

★ Bicategory
==Dagger category==

★ Dagger symmetric monoidal category

★ Dagger compact category

★ Strongly ribbon category
==Monoidal category==

★ Identity object

★ Closed monoidal category

★ Braided monoidal category
==Cartesian closed category

Structure (category theory)==

★ Semigroupoid

★ Comma category

★ Localization of a category

★ Enriched category

★ Bicategory

Topoi, toposes

★ Topos

★ Sheaf

★ Gluing axiom

★ Descent (category theory)

★ Grothendieck topology

★ Introduction to topos theory

★ Subobject classifier

★ Pointless topology

★ Heyting algebra
See also: Abstract nonsense, Homological algebra