Lemma coproduct_of_functors_nat_trans {I : UU} {C D : category} (CP : Coproducts I D) {F G : I → C ⟶ D} (α : ∏ i : I, nat_trans (F i) (G i)) : nat_trans (coproduct_of_functors I C D CP F) (coproduct_of_functors I C D CP G). Proof. use make_nat_trans. - intro c. use CoproductOfArrows. exact (λ i, α i c). - apply coproduct_of_functors_nat_trans_aux. Defined.
Require Import UniMath.Foundations.All. Require Import UniMath.MoreFoundations.All. Require Import UniMath.CategoryTheory.Core.Categories. Require Import UniMath.CategoryTheory.Core.NaturalTransformations. Require Import UniMath.CategoryTheory.Core.Functors. Require Import UniMath.CategoryTheory.Core.Isos. Require Import UniMath.CategoryTheory.Limits.Coproducts. Require Import UniMath.CategoryTheory.Limits.Graphs.Limits. Require Import UniMath.CategoryTheory.Limits.Graphs.Colimits. Require Import UniMath.CategoryTheory.Chains.All.