proposition: Lemma correct_hom_on_id {A B : precategory} (F : catiso A B) : forall a, identity ((eqweqmap (catiso_to_precategory_ob_path F)) a) = (eqweqmap (correct_hom F a a)) (identity (F a)).
proof: Proof. intros a. apply pathsinv0. eapply pathscomp0. apply eqweq_correct_hom_is_comp. induction (eqweq_ob_path_is_functor_app F a). simpl. rewrite 2 id_right. 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