proposition: Lemma functor_on_is_inverse_in_precat {C C' : precategory} (F : functor C C') {a b : ob C} {f : a --> b} {g : b --> a} (H : is_inverse_in_precat f g) : is_inverse_in_precat (# F f) (# F g).
proof: Proof. use make_is_inverse_in_precat. - rewrite <- functor_comp. rewrite (is_inverse_in_precat1 H). apply functor_id. - rewrite <- functor_comp. rewrite (is_inverse_in_precat2 H). apply functor_id. Qed.
imports: UniMath.Foundations.PartD UniMath.Foundations.Propositions UniMath.Foundations.Sets UniMath.MoreFoundations.PartA UniMath.MoreFoundations.Univalence UniMath.MoreFoundations.Tactics UniMath.CategoryTheory.Core.Categories UniMath.CategoryTheory.Core.Isos UniMath.CategoryTheory.Core.TransportMorphisms UniMath.CategoryTheory.Core.Univalence