Definition isLimFunctor_is_pointwise_Lim (X : [A,C]) (R : cone D X) (H : isLimCone D X R) : ∏ a, isLimCone (diagram_pointwise D a) _ (cone_pointwise X R a). Proof. intro a. apply (is_z_iso_isLim _ (HCg a)). set (XR := isLim_is_z_iso D LimFunctorCone X R H). apply (nat_trafo_pointwise_z_iso_if_z_iso _ _ XR). 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.