Definition CoproductOfArrowsInclusion_comp {I J K: UU} {C : category} {a : I -> C} {b : J -> C} {c : K -> C} (CCI : Coproducts I C) (CCJ : Coproducts J C) (CCK : Coproducts K C) {inclI : I -> J} {inclJ : J -> K} (f : ∏ i, a i --> b (inclI i)) (g : ∏ j, b j --> c (inclJ j)) : CoproductOfArrowsInclusion inclI (CCI _) (CCJ _) f · CoproductOfArrowsInclusion inclJ (CCJ _) (CCK _) g = CoproductOfArrowsInclusion (λ i, inclJ (inclI i)) (CCI _) (CCK _) (λ i, f i · g (inclI i)).
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.