Definition chain_mor {C : category} (c : chain C) {i j} : i < j -> C⟦dob c i, dob c j⟧. Proof. induction j as [|j IHj]. - intros Hi0; destruct (negnatlthn0 0 Hi0). - intros Hij. destruct (natlehchoice4 _ _ Hij) as [|H]. + apply (IHj h · dmor c (idpath (S j))). + apply dmor, (maponpaths S H). Defined.
Require Import UniMath.Foundations.PartA. Require Import UniMath.Foundations.NaturalNumbers. Require Import UniMath.MoreFoundations.Tactics. Require Import UniMath.CategoryTheory.Core.Categories. Require Import UniMath.CategoryTheory.Core.Functors. Require Import UniMath.CategoryTheory.Limits.Graphs.Colimits. Require Import UniMath.CategoryTheory.Limits.Graphs.Limits. Require Import UniMath.CategoryTheory.Limits.Initial.