Lemma id_is_weak_equiv (C : category) : is_weak_equiv (functor_identity C). Proof. split. - apply identity_functor_is_essentially_surjective. - apply identity_functor_is_fully_faithful. Qed.
Require Import UniMath.Foundations.All. Require Import UniMath.MoreFoundations.All. Require Import UniMath.CategoryTheory.Core.Categories. Require Import UniMath.CategoryTheory.Core.Functors. Require Import UniMath.CategoryTheory.Core.Isos. Require Import UniMath.CategoryTheory.Core.Univalence. Require Import UniMath.CategoryTheory.FunctorCategory. Require Import UniMath.CategoryTheory.catiso. Require Import UniMath.CategoryTheory.whiskering. Require Import UniMath.CategoryTheory.PrecompEquivalence.