Category:Definitions/Category Theory
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This category contains definitions related to Category Theory.
Related results can be found in Category: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 14 subcategories, out of 14 total.
A
C
- Definitions/Chain Complexes (2 P)
D
E
F
I
L
M
N
P
- Definitions/Pullbacks (3 P)
S
- Definitions/Sheaves (2 P)
- Definitions/Stacks (5 P)
Pages in category "Definitions/Category Theory"
The following 189 pages are in this category, out of 189 total.
A
C
- Definition:Cartesian Closed Category
- Definition:Category
- Definition:Category Theory
- Definition:Category Theory/Also known as
- Definition:Category with Binary Products
- Definition:Category with Exponentials
- Definition:Category with Finite Products
- Definition:Category with Products
- Definition:Category with Products/Binary
- Definition:Category with Products/Finite
- Definition:Chain Complex
- Definition:Cocone
- Definition:Codomain Functor
- Definition:Codomain of Morphism
- Definition:Coequalizer
- Definition:Coimage (Category Theory)
- Definition:Colimit
- Definition:Commutative Diagram
- Definition:Commutative Square
- Definition:Complete Category
- Definition:Composable Morphisms
- Definition:Composite Functor
- Definition:Composite Morphism
- Definition:Composition Functor on Slice Categories
- Definition:Composition of Functors
- Definition:Composition of Morphisms
- Definition:Cone (Category Theory)
- Definition:Constant (Category Theory)
- Definition:Constant Presheaf
- Definition:Continuous Functor
- Definition:Contravariant Hom Functor
- Definition:Contravariant Representable Functor
- Definition:Coproduct
- Definition:Coterminal Object
- Definition:Covariant Hom Functor
- Definition:Covariant Representable Functor
D
E
- Definition:Edge (Category Theory)
- Definition:Embedding of Categories
- Definition:Enough Constants
- Definition:Enough Injectives
- Definition:Enough Projectives
- Definition:Epi-Mono Factorization
- Definition:Epimorphism (Category Theory)
- Definition:Equalizer
- Definition:Equivalence of Categories
- Definition:Equivalence of Categories/Equivalent Categories
- Definition:Equivalent Categories
- Definition:Evaluation Morphism
- Definition:Exact Chain Complex
- Definition:Exactness of Chain Complex at Object
- Definition:Exponential (Category Theory)
- Definition:Exponential (Category Theory)/Evaluation
- Definition:Exponential (Category Theory)/Transpose
- Definition:Exponential Transpose
- Definition:Exponentiation Functor
F
- Definition:Faithful Functor
- Definition:Fibred Category
- Definition:Filtered Category
- Definition:Final Object
- Definition:Finite Category
- Definition:Finite Product (Category Theory)
- Definition:Full Functor
- Definition:Full Subcategory
- Definition:Fully Faithful Functor
- Definition:Functor
- Definition:Functor Creating Colimits
- Definition:Functor Creating Limits
- Definition:Functor Preserving Limits
H
I
- Definition:Identity Functor
- Definition:Identity Morphism
- Definition:Image (Category Theory)
- Definition:Initial Object
- Definition:Injective on Morphisms
- Definition:Injective on Objects
- Definition:Inverse Morphism
- Definition:Isomorphic Categories
- Definition:Isomorphism (Category Theory)
- Definition:Isomorphism of Categories
- Definition:Isomorphism of Categories/Isomorphic Categories
K
L
- Definition:Language of Category Theory
- Definition:Left Adjoint Functor
- Definition:Left Exact Functor
- Definition:Limit (Category Theory)
- Definition:Limit (Category Theory)/Finite Limit
- Definition:Limit of Sets (Category Theory)
- Definition:Limit of Topological Spaces
- Definition:Limit Topology
- Definition:Local Membership Relation
- Definition:Locally Small Category
M
- Definition:Metacategory
- Definition:Metagraph
- Definition:Monomorphism (Category Theory)
- Definition:Morphism
- Definition:Morphism Functor
- Definition:Morphism in Category
- Definition:Morphism of Category
- Definition:Morphism of Chain Complexes
- Definition:Morphism of Cocones
- Definition:Morphism of Cones
- Definition:Morphisms-Only Metacategory
N
O
P
- Definition:Path (Category Theory)
- Definition:Pointed Category
- Definition:Pre-Abelian Category
- Definition:Preadditive Category
- Definition:Product (Category Theory)
- Definition:Product (Category Theory)/Binary Product
- Definition:Product (Category Theory)/General Definition
- Definition:Product (Category Theory)/General Definition/Finite Product
- Definition:Product Category
- Definition:Product Functor
- Definition:Product of Morphisms
- Definition:Projection (Category Theory)
- Definition:Projection Functor
- Definition:Projective Object
- Definition:Property of Morphisms
- Definition:Property of Morphisms Stable Under Composition
- Definition:Property of Morphisms Stable Under Pullback
- Definition:Pullback (Category Theory)
R
S
- Definition:Section (Category Theory)
- Definition:Slice Functor
- Definition:Small Category
- Definition:Source (Category Theory)
- Definition:Split Epimorphism
- Definition:Split Monomorphism
- Definition:Stack
- Definition:Subcategory
- Definition:Subobject
- Definition:Surjective on Morphisms
- Definition:Surjective on Objects