Lemma is_nat_trans_coproduct_nat_trans_in_data i : is_nat_trans _ _ (coproduct_nat_trans_in_data i). Proof. intros c c' f; apply pathsinv0. now eapply pathscomp0;[apply (CoproductOfArrowsIn I _ (HD (λ i, (F i) c)))|]. Qed.
Require Import UniMath.Foundations.All. Require Import UniMath.MoreFoundations.All. 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.ProductCategory. Require Import UniMath.CategoryTheory.Limits.Graphs.Colimits. Require Import UniMath.CategoryTheory.whiskering.