Definition three_mor_eq'' {C : category} {x y : three C} {f g : x --> y} (Hb: pr1 f = pr1 g) (H11: three_mor11 f = three_mor11 g) : f = g. Proof. use three_mor_eq'. - exact (base_paths _ _ Hb). - exact H11. Qed. Section three_colimits. Context {C : category}. Context {g : graph}. Context (d : diagram g (three C)). Local Definition three_middle_diagram : diagram g C. Proof. exists (λ v, three_ob1 (dob d v)). intros u v e. exact (three_mor11 (dmor d e)). Defined.
Require Import UniMath.MoreFoundations.All. Require Import UniMath.CategoryTheory.Core.Prelude. Require Import UniMath.CategoryTheory.PrecategoryBinProduct. Require Import UniMath.CategoryTheory.DisplayedCats.Core. Require Import UniMath.CategoryTheory.DisplayedCats.Total. Require Import UniMath.CategoryTheory.Limits.Graphs.Colimits. Require Import UniMath.CategoryTheory.DisplayedCats.Examples.Arrow.