Definition colim_nat_trans_in_data v : [A, C, hsC] ⟦ dob D v, ColimFunctor ⟧. Proof. refine (tpair _ _ _). - intro a; exact (colimIn (HCg a) v). - abstract (intros a a' f; now apply pathsinv0, (colimOfArrowsIn _ _ (HCg a) (HCg a'))). 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.