Definition lan_precomposition_counit_natural_trans {F G : C₂ ⟶ D} (τ : F ⟹ G) : nat_trans_comp _ _ _ (lan_nat_trans ColimsD P (pre_whisker P τ : P ∙ F ⟹ P ∙ G)) (lan_precomposition_counit_data G) = nat_trans_comp _ _ _ (lan_precomposition_counit_data F) τ.
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.