Lemma functor_is_inverse_in_precat_inv_from_z_iso {C D : precategory} {c c' : ob C} (F : functor C D) (f : z_iso c c') : is_inverse_in_precat (# F f) (# F (inv_from_z_iso f)). Proof. apply functor_on_is_inverse_in_precat. split. - apply z_iso_inv_after_z_iso. - apply z_iso_after_z_iso_inv. 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.