A functor is said to be representable if there exists and an isomorphism? .
Properties
Theorem 9.5.9
If is a category, then the type “F is representable” is a mere proposition.
Proof. By definition “F is representable” is just the fiber of over . Since is an ambedding by Corollary 9.5.7 (see Yoneda lemma), this fiber is a mere proposition.