proposition: Lemma functor_preserves_is_retraction {a b : C} (f : retraction b a) : is_retraction (#F (retraction_section f)) (#F f).
proof: Proof. refine (!functor_comp _ _ _ @ _). refine (maponpaths _ (retraction_is_retraction f) @ _). apply functor_id. Qed.
imports: UniMath.Foundations.All UniMath.MoreFoundations.All UniMath.CategoryTheory.Core.Categories UniMath.CategoryTheory.Core.Functors