Lemma has_homsets_coslice_precat : has_homsets (coslice_precat). Proof. intros a b. induction a as [a f]; induction b as [b g]; simpl. apply (isofhleveltotal2 2); [ apply C | intro h]. apply isasetaprop; apply C. Qed.
Require Import UniMath.Foundations.PartA. Require Import UniMath.Foundations.PartD. Require Import UniMath.MoreFoundations.Tactics. Require Import UniMath.CategoryTheory.Core.Categories. Require Import UniMath.CategoryTheory.Core.Functors. Require Import UniMath.CategoryTheory.Core.Isos. Require Import UniMath.CategoryTheory.DisplayedCats.Core. Require Import UniMath.CategoryTheory.DisplayedCats.Total.