representable functor

English

Etymology

If a representable functor is naturally isomorphic to a hom functor ${\displaystyle {\mbox{Hom}}(C,-)}$ or ${\displaystyle {\mbox{Hom}}(-,C)}$, then the object C is said to represent that representable functor.

Noun

representable functor (plural representable functors)

1. (category theory) A functor from some category to the category of sets (Set) which is naturally isomorphic to a hom functor.

Synonyms

• representable presheaf