Lemma functor_preserves_is_retraction {a b : C} (f : retraction b a) : is_retraction (#F (retraction_section f)) (#F f). Proof. refine (!functor_comp _ _ _ @ _). refine (maponpaths _ (retraction_is_retraction f) @ _). apply functor_id. 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.