List of category theory topics
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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 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
- 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
Limits
- 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
Limits
- Limit (category theory)
- *Product (category theory)
- *Equalizer
- *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
- Identity object
Topoi, Toposes
Topoi, Toposes
- Topos
- Sheaf
- Gluing axiom
- Descent (category theory)
- Grothendieck topology
- Introduction to topos theory
- Subobject classifier
- Pointless topology
- Heyting algebra
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