Definition internal_relation {C : category} (x : C) : UU := ∑ (r : C) (s t : r --> x), ∏ (w : C) (f g : w --> r), f · s = g · s → f · t = g · t → f = g.
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.