Definition mapcocone {g : graph} (d : diagram g C) {x : C} (dx : cocone d x) : cocone (mapdiagram d) (F x). Proof. use make_cocone. - simpl; intro n. exact (#F (coconeIn dx n)). - abstract (intros u v e; simpl; rewrite <- functor_comp; apply maponpaths, (coconeInCommutes dx _ _ e)). Defined.
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.