Lemma functor_isaset (C C' : precategory_data) (hs : has_homsets C') (hsC' : isaset C') : isaset (functor C C'). Proof. change isaset with (isofhlevel 2). apply isofhleveltotal2. apply (functor_data_isaset C C' hs hsC'). intros x. apply isasetaprop. apply (isaprop_is_functor C C' hs). Qed.
Require Import UniMath.Foundations.PartD. Require Import UniMath.Foundations.Propositions. Require Import UniMath.Foundations.Sets. Require Import UniMath.MoreFoundations.PartA. Require Import UniMath.MoreFoundations.Univalence. Require Import UniMath.MoreFoundations.Tactics. Require Import UniMath.CategoryTheory.Core.Categories. Require Import UniMath.CategoryTheory.Core.Isos. Require Import UniMath.CategoryTheory.Core.TransportMorphisms. Require Import UniMath.CategoryTheory.Core.Univalence.