The story
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.
Etymology from Wiktionary, CC BY-SA 4.0.
representable functor
Today it means: A functor from some category to the category of sets (Set) which is naturally isomorphic to a hom functor. Full definition →