proposition: Lemma catiso_to_precategory_mor_path_funext {A B : precategory_data} (F : catiso A B) : (precategory_morphisms (C:=A)) = transportb (λ T, T -> T -> UU) (catiso_to_precategory_ob_path F) (precategory_morphisms (C:=B)).
proof: Proof. apply (pr1 (weqfunextsec _ _ _)). intros a. apply (pr1 (weqfunextsec _ _ _)). intros a'. apply (catiso_to_precategory_mor_path F). 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