Lemma functor_preserves_is_idempotent {c : C} (f : idempotent c) : is_idempotent (#F f). Proof. refine (!functor_comp _ _ _ @ _). apply maponpaths. apply idempotent_is_idempotent. Qed.
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.OppositeCategory.Core.