Definition internal_iseqrel_mor_eqrel {C : category} {x : C} (R : internal_eqrel x) (w : C) : eqrel (w --> x). Proof. use make_eqrel. - exact (internal_relation_to_arr_hrel R w). - repeat split. + apply (internal_iseqrel_internal_eqrel R). + apply (internal_iseqrel_internal_eqrel R). + apply (internal_iseqrel_internal_eqrel R). Defined.
Require Import UniMath.Foundations.All. Require Import UniMath.MoreFoundations.All. Require Import UniMath.CategoryTheory.Core.Prelude. Require Import UniMath.CategoryTheory.Limits.Pullbacks. Require Import UniMath.CategoryTheory.Limits.Coequalizers. Require Import UniMath.CategoryTheory.RegularAndExact.RegularCategory.