Lemma roundtrip2_iso_z_iso {C : category} {b c : C} (f: z_iso b c) : iso_to_z_iso (z_iso_to_iso f) = f. Proof. destruct f as [f H]. use total2_paths_f. - apply idpath. - apply isaprop_is_z_isomorphism. Qed.
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.