proposition: Lemma free_functor_is_morphism {X X' : hSet} (f : X → X') : is_algebraic_theory_morphism (free_functor_morphism_data f).
proof: Proof. use make_is_algebraic_theory_morphism. - intros n t. now induction t. - intros m n s t. now induction s. Qed.
imports: UniMath.Foundations.All UniMath.MoreFoundations.All UniMath.CategoryTheory.Adjunctions.Core UniMath.CategoryTheory.Categories.HSET.Core UniMath.CategoryTheory.Categories.HSET.Limits UniMath.CategoryTheory.Core.Categories UniMath.CategoryTheory.Core.Functors UniMath.CategoryTheory.Core.Isos UniMath.CategoryTheory.Core.NaturalTransformations UniMath.CategoryTheory.coslicecat UniMath.CategoryTheory.DisplayedCats.Total UniMath.CategoryTheory.Equivalences.Core UniMath.CategoryTheory.Limits.Graphs.Limits UniMath.Combinatorics.StandardFiniteSets UniMath.Combinatorics.Vectors UniMath.AlgebraicTheories.AlgebraCategory UniMath.AlgebraicTheories.AlgebraCategoryCore UniMath.AlgebraicTheories.AlgebraicTheories UniMath.AlgebraicTheories.AlgebraicTheoryCategoryCore UniMath.AlgebraicTheories.AlgebraicTheoryMorphisms UniMath.AlgebraicTheories.AlgebraMorphisms UniMath.AlgebraicTheories.Algebras