Lemma z_iso_comp_right_isweq {C : precategory} {a b : ob C} (h : z_iso a b) (c : C) : isweq (fun f : b --> c => h · f). Proof. intros. apply (isweq_iso _ (λ g, inv_from_z_iso h · g)). { intros f. use (_ @ maponpaths (λ m, m · f) (pr2 (pr2 (pr2 h))) @ _). { apply assoc. } { apply id_left. } } { intros g. use (_ @ maponpaths (λ m, m · g) (pr1 (pr2 (pr2 h))) @ _). { apply assoc. } { apply id_left. } } Defined.
Require Import UniMath.Foundations.PartA. Require Import UniMath.Foundations.Propositions. Require Import UniMath.Foundations.Sets. Require Import UniMath.MoreFoundations.Tactics. Require Import UniMath.CategoryTheory.Core.Categories.