Lemma fully_faithful_sub_precategory_inclusion : fully_faithful (sub_precategory_inclusion C (full_sub_precategory C')). Proof. apply full_and_faithful_implies_fully_faithful. split. - apply full_sub_precategory_inclusion. - apply faithful_sub_precategory_inclusion. 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.