proposition: Lemma is_univalent_algebra_cat (T : algebraic_theory) : is_univalent (algebra_cat T).
proof: Proof. refine (is_univalent_fiber_cat _ _ _). unfold algebra_disp_cat. repeat use is_univalent_sigma_disp. - apply is_univalent_disp_cartesian'. apply is_univalent_HSET. - exact is_univalent_disp_algebra_data_full_disp_cat. - exact is_univalent_disp_algebra_full_disp_cat. Qed.
imports: UniMath.Foundations.All UniMath.MoreFoundations.All UniMath.CategoryTheory.Categories.HSET.Core UniMath.CategoryTheory.Categories.HSET.Univalence UniMath.CategoryTheory.Core.Categories UniMath.CategoryTheory.Core.Isos UniMath.CategoryTheory.Core.Univalence UniMath.CategoryTheory.DisplayedCats.Core UniMath.CategoryTheory.DisplayedCats.Constructions UniMath.CategoryTheory.DisplayedCats.Examples.Cartesian UniMath.CategoryTheory.DisplayedCats.Examples.Sigma UniMath.CategoryTheory.DisplayedCats.Fiber UniMath.CategoryTheory.DisplayedCats.Total UniMath.CategoryTheory.DisplayedCats.Univalence UniMath.CategoryTheory.DisplayedCats.Fibrations UniMath.AlgebraicTheories.Algebras UniMath.AlgebraicTheories.AlgebraMorphisms UniMath.AlgebraicTheories.AlgebraCategoryCore UniMath.AlgebraicTheories.AlgebraicTheories UniMath.AlgebraicTheories.AlgebraicTheoryMorphisms UniMath.AlgebraicTheories.AlgebraicTheoryCategoryCore UniMath.AlgebraicTheories.AlgebraicTheoryCategory