Definition z_iso_from_lim_to_lim {C : precategory} {g : graph} {d : diagram g C} (CC CC' : LimCone d) : z_iso (lim CC) (lim CC'). Proof. use make_z_iso. - apply limArrow, limCone. - apply limArrow, limCone. - abstract (now split; apply pathsinv0, lim_endo_is_identity; intro u; rewrite <- assoc, limArrowCommutes; eapply pathscomp0; try apply limArrowCommutes). Defined.
Require Import UniMath.Foundations.PartD. Require Import UniMath.Foundations.Propositions. Require Import UniMath.Foundations.Sets. Require Import UniMath.MoreFoundations.Tactics. Require Import UniMath.MoreFoundations.Propositions. Require Import UniMath.CategoryTheory.Core.Categories. Require Import UniMath.CategoryTheory.Core.Functors. Require Import UniMath.CategoryTheory.Core.Isos. Require Import UniMath.CategoryTheory.Core.NaturalTransformations. Require Import UniMath.CategoryTheory.Core.Univalence. Require Import UniMath.CategoryTheory.Adjunctions.Core. Require Import UniMath.CategoryTheory.FunctorCategory. Require Import UniMath.CategoryTheory.Limits.Graphs.Colimits. Import UniMath.CategoryTheory.opp_precat.