Definition subprecategory_of_epis : sub_precategories C. Proof. use tpair. split. - exact hsubtype_obs_isEpi. - exact hsubtype_mors_isEpi. - cbn. unfold is_sub_precategory. cbn. split. + intros a tt. exact (identity_isEpi C). + apply isEpi_comp. Defined.
Require Import UniMath.Foundations.PartD. Require Import UniMath.Foundations.Propositions. Require Import UniMath.Foundations.Sets. Require Import UniMath.CategoryTheory.Core.Categories. Require Import UniMath.CategoryTheory.Core.Isos. Require Import UniMath.CategoryTheory.Core.NaturalTransformations. Require Import UniMath.CategoryTheory.FunctorCategory. Require Import UniMath.CategoryTheory.Subcategory.Core. Require Import UniMath.CategoryTheory.Core.Functors.