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. 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.
Require Import UniMath.Foundations.PartD. Require Import UniMath.Foundations.Propositions. Require Import UniMath.Foundations.Sets. Require Import UniMath.MoreFoundations.PartA. Require Import UniMath.MoreFoundations.Univalence. Require Import UniMath.MoreFoundations.Tactics. Require Import UniMath.CategoryTheory.Core.Categories. Require Import UniMath.CategoryTheory.Core.Isos. Require Import UniMath.CategoryTheory.Core.TransportMorphisms. Require Import UniMath.CategoryTheory.Core.Univalence.