A structure-preserving map between categories: sends objects to objects, morphisms to morphisms, preserves composition and identities. Examples: forgetful Grp → Set, π₁ from pointed Top to Grp.
Functor F: C → D
Related concepts
- Category
- Morphism (arrow) f: A → B
- Natural transformation η: F ⇒ G
- Limit and colimit
- Adjunction F ⊣ G
- Yoneda lemma
- Monad
- Kan extension
- Sheaf
- Derived category D(𝒜)
- Adjoint functors
- Monoidal category
- Simplicial set
- Abelian category
- Ends and coends
- Grothendieck construction
- Atiyah–Segal topological quantum field theory
- Wightman axioms
- Spin foam (path-integral)