Definition z_iso_from_lim_to_lim {J C : precategory} {F : functor J C} (CC CC' : LimCone F) : 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.Isos. Require Import UniMath.CategoryTheory.Core.NaturalTransformations. Require Import UniMath.CategoryTheory.Core.Univalence. Require Import UniMath.CategoryTheory.Core.Functors. Require Import UniMath.CategoryTheory.FunctorCategory.