Category:Category Theory
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This category contains results about Category Theory.
Definitions specific to this category can be found in Definitions/Category Theory.
Category theory is the branch of abstract algebra which studies categories.
It can be described as the theory of functors.
Subcategories
This category has the following 29 subcategories, out of 29 total.
A
- Abelian Categories (1 P)
C
- Category of Lattices (4 P)
- Category of Semilattices (1 P)
D
- Direct Sums (1 P)
E
- Embeddings of Categories (1 P)
F
- Free Monoids (2 P)
- Functors (19 P)
G
- Grothendieck Universes (6 P)
- Groupoids (empty)
L
M
N
- Natural Transformations (empty)
O
- Objects (Category Theory) (empty)
P
- Preadditive Categories (4 P)
R
- Retractions (Category Theory) (empty)
S
U
Pages in category "Category Theory"
The following 62 pages are in this category, out of 62 total.
C
- Category Axioms are Self-Dual
- Category has Finite Limits iff Finite Products and Equalizers
- Category has Products and Equalizers iff Pullbacks and Terminal Object
- Category Induces Preorder
- Category of Pointed Sets is Category
- Cayley's Theorem (Category Theory)
- Characterization of Metacategory via Equations
- Coequalizer is Epimorphism
- Composite Functor is Functor
- Composition of Functors is Associative
- Composition with Zero Morphism is Zero Morphism
- Contravariant Hom Functor maps Colimits to Limits
- Covariant Hom Functor is Continuous
- Covariant Hom Functor is Functor
E
I
- Identity Functor is Functor
- Identity Functor is Left Identity
- Identity Functor is Right Identity
- Identity Morphism is Unique
- Identity Morphism of Product
- Initial Object is Unique
- Injective iff Projective in Dual Category
- Inverse Morphism is Unique
- Isomorphism (Category Theory) is Epic
- Isomorphism (Category Theory) is Monic