List of category theory topics
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This is a list of category theory topics, by Wikipedia page.
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Specific categories
- Category of sets
- Category of 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
Morphisms
- 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
- Monad (category theory)
- Comonad
- Combinatorial species
- Exact functor
- Derived functor
- Enriched functor
Limits
Additive structure
- Preadditive category
- Additive category
- Pre-Abelian category
- Abelian category
- Injective cogenerator
- Derived category
- Triangulated category
- Model category
Monoidal category
Cartesian closed category
Structure (category theory)
Toposes
- Sheaf
- Gluing axiom
- Descent (category theory)
- Grothendieck topology
- Introduction to topos theory
- Subobject classifier
- Pointless topology
- Heyting algebra
See also: abstract nonsense, homological algebra