Definition base_category_z_iso_fam_weq (F₀ G₀ : base_category) : is_univalent D → F₀ ~ G₀ ≃ (∏ (x : C), z_iso (F₀ x) (G₀ x)). Proof. intros HD. apply weqonsecfibers. intros x. exists idtoiso. apply HD. Defined.
Require Import UniMath.Foundations.PartD. Require Import UniMath.Foundations.UnivalenceAxiom. Require Import UniMath.MoreFoundations.Propositions. Require Import UniMath.CategoryTheory.Core.Categories. Require Import UniMath.CategoryTheory.Core.Isos. Require Import UniMath.CategoryTheory.Core.Univalence. Require Import UniMath.CategoryTheory.Categories.HSET.Core. Require Import UniMath.CategoryTheory.Core.Functors. Require Import UniMath.CategoryTheory.FunctorCategory. Require Import UniMath.CategoryTheory.Monads.Monads. Require Import UniMath.CategoryTheory.DisplayedCats.Core. Require Import UniMath.CategoryTheory.DisplayedCats.Total. Require Import UniMath.CategoryTheory.DisplayedCats.Isos. Require Import UniMath.CategoryTheory.DisplayedCats.Univalence. Require Import UniMath.CategoryTheory.DisplayedCats.Constructions.