Definition subprecategory_of_monics : sub_precategories C. Proof. use tpair. split. - exact hsubtype_obs_isMonic. - exact hsubtype_mors_isMonic. - cbn. unfold is_sub_precategory. cbn. split. + intros a tt. exact (identity_isMonic C). + apply isMonic_comp. Defined.
Require Import UniMath.Foundations.All. Require Import UniMath.MoreFoundations.All. Require Import UniMath.CategoryTheory.Categories.HSET.Core. Require Import UniMath.CategoryTheory.Core.Categories. Require Import UniMath.CategoryTheory.Core.Functors. Require Import UniMath.CategoryTheory.Core.Isos. Require Import UniMath.CategoryTheory.Core.NaturalTransformations. Require Import UniMath.CategoryTheory.Core.Univalence. Require Import UniMath.CategoryTheory.covyoneda. Require Import UniMath.CategoryTheory.FunctorCategory. Require Import UniMath.CategoryTheory.Subcategory.Core.