proposition: Lemma eqweq_fully_faithful_is_functor_app {A B : precategory_data} (F : catiso A B) : forall a a' : A, eqweqmap (catiso_fully_faithful_path F a a') = catiso_fully_faithful_weq F _ _.
proof: Proof. intros a a'. unfold catiso_fully_faithful_path. assert (W := (@homotweqinvweq _ _ (univalence (a --> a') (F a --> F a')))). simpl in W. rewrite W. reflexivity. Defined.
imports: UniMath.Foundations.PartD UniMath.Foundations.Propositions UniMath.Foundations.Sets UniMath.Foundations.UnivalenceAxiom UniMath.MoreFoundations.All UniMath.CategoryTheory.Core.Categories UniMath.CategoryTheory.Core.Isos UniMath.CategoryTheory.Core.Univalence UniMath.CategoryTheory.Core.Functors UniMath.CategoryTheory.Core.Setcategories UniMath.CategoryTheory.whiskering UniMath.CategoryTheory.Adjunctions.Core UniMath.CategoryTheory.Equivalences.Core UniMath.CategoryTheory.Equivalences.FullyFaithful