Lemma isiso_from_Initial_to_Initial (O O' : Initial) : is_iso (InitialArrow O (InitialObject O')). Proof. apply (is_iso_qinv _ (InitialArrow O' (InitialObject O))). split; apply pathsinv0, InitialEndo_is_identity. Defined.
Require Import UniMath.Foundations.PartD. Require Import UniMath.Foundations.Propositions. Require Import UniMath.Foundations.Sets. Require Import UniMath.MoreFoundations.Tactics. Require Import UniMath.CategoryTheory.Core.Categories. Require Import UniMath.CategoryTheory.Core.Isos. Require Import UniMath.CategoryTheory.Limits.Graphs.Colimits. Require Import UniMath.CategoryTheory.Limits.Graphs.EqDiag. Require Import UniMath.CategoryTheory.Limits.Initial. Lemma ArrowsFromInitial (I : Initial) (a : C) (f g : C⟦InitialObject I,a⟧) : f = g.