proposition: Lemma is_univalent_disp_functor_alg : is_univalent_disp disp_cat_functor_alg.
proof: Proof. use is_univalent_disp_from_SIP_data. - apply isaset_functor_alg_ob. - unfold functor_alg_mor. intros x a a' H H'. rewrite functor_id in H'. rewrite id_left in H'. rewrite id_right in H'. apply H'. Defined.
imports: UniMath.Foundations.Sets UniMath.MoreFoundations.PartA UniMath.CategoryTheory.Core.Categories UniMath.CategoryTheory.Core.Functors UniMath.CategoryTheory.Core.Isos UniMath.CategoryTheory.Core.NaturalTransformations UniMath.CategoryTheory.Core.Univalence UniMath.CategoryTheory.PrecategoryBinProduct UniMath.CategoryTheory.Categories.HSET.Core UniMath.CategoryTheory.Monads.Monads UniMath.CategoryTheory.PrecategoryBinProduct UniMath.CategoryTheory.DisplayedCats.Core UniMath.CategoryTheory.DisplayedCats.Total UniMath.CategoryTheory.DisplayedCats.Isos UniMath.CategoryTheory.DisplayedCats.Univalence UniMath.CategoryTheory.DisplayedCats.Constructions UniMath.CategoryTheory.DisplayedCats.Limits UniMath.CategoryTheory.DisplayedCats.Fiber UniMath.CategoryTheory.DisplayedCats.Fibrations UniMath.CategoryTheory.DisplayedCats.SIP UniMath.CategoryTheory.DisplayedCats.Examples.Reindexing UniMath.CategoryTheory.DisplayedCats.Examples.Sigma UniMath.CategoryTheory.Limits.Graphs.Colimits UniMath.CategoryTheory.Limits.Graphs.Limits