proposition: Lemma Functor_eq_map_isweq {A B: category} {F G:[A,B]} : isweq (Functor_eq_map F G).
proof: Proof. Abort. Hypothesis Functor_eq_map_isweq : ∏ (A B: category) (F G:[A,B]), isweq (Functor_eq_map F G). Arguments Functor_eq_map_isweq {_ _ _ _} _. Lemma Functor_eq_weq {A B: category} (F G:[A,B]) : F = G ≃ ∑ (ob : ∏ a, F ◾ a = G ◾ a), ∏ a a' f, transportf (λ k, k --> G ◾ a') (ob a) (transportf (λ k, F ◾ a --> k) (ob a') (F ▭ f)) = G ▭ f. Proof. exact (make_weq _ Functor_eq_map_isweq). Defined.
imports: UniMath.Foundations.Preamble UniMath.CategoryTheory.Core.Categories UniMath.CategoryTheory.Core.Isos UniMath.CategoryTheory.Core.Functors UniMath.CategoryTheory.RepresentableFunctors.Precategories UniMath.MoreFoundations.Tactics UniMath.CategoryTheory.opp_precat UniMath.CategoryTheory.yoneda UniMath.CategoryTheory.Categories.HSET.Core