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Template:Category theory

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Category theory

Key concepts

Key concepts

Category
Adjoint functors
Commutative diagram
Concrete category
Functor
Morphism
Natural transformation
Universal property

Universal constructions

Limits	Terminal objects Products Equalizers Kernels Pullbacks Inverse limit
Colimits	Initial objects Coproducts Coequalizers Cokernels and quotients Pushout Direct limit

Algebraic categories

Sets
Relations
Magmas
Groups
Abelian groups
Rings (Fields)
Modules (Vector spaces)

Constructions on categories

Free category
Functor category
Quotient category
Product category
Subcategory

Higher category theory

Key concepts

Categorification

Enriched category

Higher-dimensional algebra

Homotopy hypothesis

Simplex category

n-categories

Weak `n`-categories	Bicategory (pseudofunctor) Tricategory Tetracategory Kan complex ∞-groupoid ∞-topos
Strict `n`-categories	2-category (2-functor) 3-category

Categorified concepts

2-group
2-ring
E_n-ring
(Symmetric) monoidal category
n-group
n-monoid

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