Lemma z_iso_comp_left_isweq {C : precategory} {a b : ob C} (h : z_iso a b) (c : C) : isweq (fun f : c --> a => f · h). Proof. intros. apply (isweq_iso _ (λ g, g · inv_from_z_iso h)). { intros f. use (_ @ maponpaths (λ m, f · m) (pr1 (pr2 (pr2 h))) @ _). { apply pathsinv0. apply assoc. } { apply id_right. } } { intros g. use (_ @ maponpaths (λ m, g · m) (pr2 (pr2 (pr2 h))) @ _). { apply pathsinv0, assoc. } { apply id_right. } } 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.