Lemma isaprop_is_cocone_mor {C : category} {g : graph} {d : diagram g C} {c1 : C} (cc1 : cocone d c1) {c2 : C} (cc2 : cocone d c2) (f : c1 --> c2) : isaprop (is_cocone_mor cc1 cc2 f). Proof. apply impred_isaprop ; intro. apply homset_property. Qed.
Require Import UniMath.Foundations.PartD. Require Import UniMath.Foundations.Propositions. Require Import UniMath.Foundations.Sets. Require Import UniMath.MoreFoundations.Tactics. Require Import UniMath.MoreFoundations.Propositions. Require Import UniMath.CategoryTheory.Core.Categories. Require Import UniMath.CategoryTheory.Core.Functors. Require Import UniMath.CategoryTheory.Core.Isos. Require Import UniMath.CategoryTheory.Core.NaturalTransformations. Require Import UniMath.CategoryTheory.Core.Univalence. Require Import UniMath.CategoryTheory.FunctorCategory. Require Import UniMath.CategoryTheory.Adjunctions.Core.