Lemma full_sub_precategory_inclusion : full (sub_precategory_inclusion C (full_sub_precategory C')). Proof. intros a b f. apply hinhpr. unfold hfiber. exists (f,, tt). reflexivity. Defined.
Require Import UniMath.Foundations.Sets. Require Import UniMath.MoreFoundations.PartA. Require Import UniMath.CategoryTheory.Core.Categories. Require Import UniMath.CategoryTheory.Core.Isos. Require Import UniMath.CategoryTheory.Core.Univalence. Require Import UniMath.CategoryTheory.Core.Functors. Require Import UniMath.CategoryTheory.Core.NaturalTransformations. Require Import UniMath.CategoryTheory.Subcategory.Core.