Definition lifting_from_distr_law_data_on_ob {C D: category} {F: functor C C} {G: functor D D} {H: functor C D} (lambda : DistrLaw G F H H): FunctorAlg F → FunctorAlg G. Proof. intro Aa. set (A := alg_carrier _ Aa). set (a := alg_map _ Aa). set (B := H A). set (b := nat_trans_data_from_nat_trans lambda A · (# H a)). use tpair. - exact B. - exact b. 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.