Definition isColimFunctor_is_pointwise_Colim (X : [A,C]) (R : cocone D X) (H : isColimCocone D X R) : ∏ a, isColimCocone (diagram_pointwise a) _ (cocone_pointwise X R a). Proof. intro a. apply (is_z_iso_isColim _ (HCg a)). set (XR := isColim_is_z_iso D ColimFunctorCocone X R H). apply (is_functor_z_iso_pointwise_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.FunctorCategory. Require Import UniMath.CategoryTheory.Adjunctions.Core.