representable functor

English

Etymology

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

Noun

representable functor (plural representable functors)

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

Synonyms

representable presheaf

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