proposition: Lemma retractions_are_epic : Retraction f → Epic f.
proof: Proof. autounfold. intros. destruct X. constructor; intros. rewrite <- id_right. symmetry. rewrite <- id_right. transitivity (g2 ∘ (f ∘ retract0)); [ now apply compose_respects |]; transitivity (g1 ∘ (f ∘ retract0)); [| now apply compose_respects ]. reassociate_right. Qed.
imports: Category.Lib Category.Theory.Category