proposition: Lemma free_object_algebra_is_functor : is_functor free_object_algebra_functor_data.
proof: Proof. split. - intro c. apply algebra_morphism_eq. apply (functor_id G). - intros c c' c'' f f'. apply algebra_morphism_eq. refine (_ @ !algebra_mor_comp _ _). exact (functor_comp G _ _). Qed.
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