proposition: Lemma functor_preserves_is_idempotent {c : C} (f : idempotent c) : is_idempotent (#F f).
proof: Proof. refine (!functor_comp _ _ _ @ _). apply maponpaths. apply idempotent_is_idempotent. Qed.
imports: UniMath.Foundations.All UniMath.MoreFoundations.All UniMath.CategoryTheory.Core.Categories UniMath.CategoryTheory.Core.Functors