Lemma mapcocone_functor_composite {g : graph} {D : diagram g A} {a : A} (cc : cocone D a) : mapcocone (functor_composite F G) _ cc = mapcocone G _ (mapcocone F _ cc). Proof. apply subtypePath. - intros x. repeat (apply impred_isaprop; intro). apply C. - reflexivity. 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.