Definition functor_preserves_retraction {a b : C} (H : retraction b a) : retraction (F b) (F a) := _ ,, _ ,, functor_preserves_is_retraction H.
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.