proposition: Lemma make_algebraic_theory_z_iso_is_iso : is_inverse_in_precat (C := algebraic_theory_cat) make_algebraic_theory_z_iso_mor make_algebraic_theory_z_iso_inv.
proof: Proof. split; apply algebraic_theory_morphism_eq; intros n f; refine (eqtohomot _ f). - apply (z_iso_inv_after_z_iso (F n)). - apply (z_iso_after_z_iso_inv (F n)). Qed.
imports: UniMath.Foundations.All UniMath.MoreFoundations.All UniMath.CategoryTheory.Categories.HSET.Core UniMath.CategoryTheory.Core.Categories UniMath.CategoryTheory.Core.Isos UniMath.CategoryTheory.Core.Univalence UniMath.CategoryTheory.DisplayedCats.Constructions UniMath.CategoryTheory.DisplayedCats.Core UniMath.CategoryTheory.DisplayedCats.Fiber UniMath.CategoryTheory.DisplayedCats.Limits UniMath.CategoryTheory.DisplayedCats.Total UniMath.CategoryTheory.DisplayedCats.Univalence UniMath.CategoryTheory.Limits.Graphs.Colimits UniMath.CategoryTheory.Limits.Graphs.Limits UniMath.AlgebraicTheories.IndexedSetCategory UniMath.AlgebraicTheories.AlgebraicTheoryCategoryCore UniMath.AlgebraicTheories.AlgebraicTheories UniMath.AlgebraicTheories.AlgebraicTheoryMorphisms