Lemma functor_on_z_iso_inv (C C' : category) (F : functor C C') (a b : ob C) (f : z_iso a b) : functor_on_z_iso F (z_iso_inv_from_z_iso f) = z_iso_inv_from_z_iso (functor_on_z_iso F f). Proof. apply z_iso_eq; simpl. apply idpath. Defined.
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.