fact: Definition free_object_algebra_data : algebra_data free_object_theory := make_algebra_data (G c) (λ n (f : free_object_theory n) a, #G (φ_adj_inv (make_adjunction _ H) (a : stnset n → _)) f).
imports: UniMath.Foundations.All UniMath.MoreFoundations.All UniMath.CategoryTheory.Core.Categories UniMath.CategoryTheory.Core.Functors UniMath.CategoryTheory.Core.NaturalTransformations UniMath.CategoryTheory.Categories.HSET.Core UniMath.CategoryTheory.Adjunctions.Core UniMath.Combinatorics.StandardFiniteSets UniMath.AlgebraicTheories.AlgebraicTheories UniMath.AlgebraicTheories.AlgebraCategoryCore UniMath.AlgebraicTheories.Algebras UniMath.AlgebraicTheories.AlgebraMorphisms UniMath.AlgebraicTheories.AlgebraicTheoryCategoryCore