- List of category theory topics
This is a list of
category theory topics, by Wikipedia page.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 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 Morphism s*
Epimorphism
*Monomorphism
*Zero morphism
*Normal morphism
*Dual (category theory)
*Groupoid
*Image (category theory)
*Coimage
*Commutative diagram
*Cartesian morphism
*Slice category Functor s*
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)
**Equaliser (mathematics)
**Kernel (category theory)
**Pullback (category theory) ,fiber product
**Inverse limit
***Pro-finite group
*Colimit
**Coproduct
**Coequalizer
**Cokernel
**Pushout (category theory)
**Direct limit
*Biproduct
**Direct sum Additive structure
*
Preadditive category
*Additive category
*Pre-Abelian category
*Abelian category
**Exact sequence
**Exact functor
**Snake lemma
***Nine lemma
**Five lemma
***Short five lemma
**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 *
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 ,Glossary of category theory
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