Lemma univalent_category_has_groupoid_ob (C : univalent_category): isofhlevel 3 (ob C). Proof. change (isofhlevel 3 C) with (∏ a b : C, isofhlevel 2 (a = b)). intros a b. apply (isofhlevelweqb _ (tpair _ _ (pr2 C a b))). apply isaset_z_iso. Qed.
Require Import UniMath.Foundations.PartA. Require Import UniMath.Foundations.Sets. Require Import UniMath.MoreFoundations.PartA. Require Import UniMath.MoreFoundations.Tactics. Require Import UniMath.CategoryTheory.Core.Categories. Require Import UniMath.CategoryTheory.Core.Isos.