Lemma is_functor_lifting_from_distr_law_data {C D: category} {F: functor C C} {G: functor D D} {H: functor C D} (lambda : DistrLaw G F H H): is_functor (lifting_from_distr_law_data lambda). Proof. split. - intro Aa. unfold lifting_from_distr_law_data. cbn. UniMath.MoreFoundations.Tactics.show_id_type. use total2_paths_f. 2: { apply homset_property. } cbn. apply functor_id. - intros Aa Bb Cc f g. unfold lifting_from_distr_law_data. cbn. UniMath.MoreFoundations.Tactics.show_id_type. use total2_paths_f. 2: { apply homset_property. } cbn. apply functor_comp. Qed.
Require Import UniMath.Foundations.Sets. Require Import UniMath.CategoryTheory.Core.Categories. Require Import UniMath.CategoryTheory.Core.Functors. Require Import UniMath.CategoryTheory.Core.NaturalTransformations. Require Import UniMath.CategoryTheory.whiskering. Require Import UniMath.CategoryTheory.FunctorAlgebras. Require Import UniMath.CategoryTheory.UnitorsAndAssociatorsForEndofunctors. Require Import UniMath.CategoryTheory.Limits.Initial. Require Import UniMath.CategoryTheory.Adjunctions.Core.