Definition lan_nat_trans_comp {C₁ C₂ D : category} (ColimsD : Colims D) (P : C₁ ⟶ C₂) {F G H : C₁ ⟶ D} (τ₁ : F ⟹ G) (τ₂ : G ⟹ H) : lan_nat_trans ColimsD P (nat_trans_comp _ _ _ τ₁ τ₂) = nat_trans_comp _ _ _ (lan_nat_trans ColimsD P τ₁) (lan_nat_trans ColimsD P τ₂).
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.Adjunctions.Core. Require Import UniMath.CategoryTheory.Limits.Graphs.Colimits. Require Import UniMath.CategoryTheory.Categories.StandardCategories. Require Import UniMath.CategoryTheory.CommaCategories. Require Import UniMath.CategoryTheory.FunctorCategory. Require Import UniMath.CategoryTheory.whiskering.