Definition shift_iter_cocone (A : C) : cocone (mapchain F (iter_chain_at A)) (F^ω A). Proof. apply make_cocone with (λ i, colimIn (CC A) (S i)). abstract (intros i _ []; exact (colimInCommutes (CC A) (S i) _ (idpath (S (S i))))). Defined.
Require Import UniMath.Foundations.All. Require Import UniMath.MoreFoundations.All. Require Import UniMath.CategoryTheory.Core.Categories. Require Import UniMath.CategoryTheory.Core.Functors. Require Import UniMath.CategoryTheory.Core.NaturalTransformations. Require Import UniMath.CategoryTheory.Core.Isos. Require Import UniMath.CategoryTheory.Adjunctions.Core. Require Import UniMath.CategoryTheory.Limits.Graphs.Colimits. Require Import UniMath.CategoryTheory.Chains.Chains. Require Import UniMath.CategoryTheory.FunctorCategory. Require Import UniMath.CategoryTheory.whiskering.