Definition 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): functor_data (FunctorAlg F) (FunctorAlg G). Proof. use make_functor_data. - apply (lifting_from_distr_law_data_on_ob lambda). - cbn. intros Aa Bb. intro h. unfold algebra_mor. use tpair. + exact (#H (pr1 h)). + apply lifting_from_distr_law_data_aux. Defined.
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.