Definition locally_univalent_two_cat (C : two_cat) : UU := ∏ (x y : C), is_univalent (hom_cat x y).
Require Import UniMath.Foundations.All. Require Import UniMath.MoreFoundations.All. Require Import UniMath.CategoryTheory.Core.Categories. Require Import UniMath.CategoryTheory.Core.Setcategories. Require Import UniMath.CategoryTheory.Core.Univalence.