proposition: Lemma functor_preserves_split_monic {C D : category} (F : functor C D) {A B : ob C} (f : C⟦A,B⟧) : is_split_monic f -> is_split_monic (# F f).
proof: Proof. intro hf. exists (#F (pr1 hf)). unfold is_retraction. now rewrite <- functor_id, <- (pr2 hf), <- functor_comp. Qed.
imports: UniMath.Foundations.PartD UniMath.Foundations.Propositions UniMath.MoreFoundations.Tactics UniMath.CategoryTheory.Core.Categories UniMath.CategoryTheory.Core.Isos UniMath.CategoryTheory.Core.Functors UniMath.CategoryTheory.Monics UniMath.CategoryTheory.Epis UniMath.CategoryTheory.Retracts