proposition: Lemma function_to_is_theory_morphism (F : A → (forgetful_functor T : hSet)) : is_algebraic_theory_morphism (function_to_theory_morphism_data F).
proof: Proof. use make_is_algebraic_theory_morphism. - easy. - intros ? ? f ?. induction f. + exact (!pr_comp _ _ _). + refine (lift_constant_eq _ _ _ _ (idpath _) @ !_). apply comp_comp. 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