proposition: Lemma is_nat_trans_monic_from_pointwise_monics (C D : category) (F G : ob (functor_category C D)) (α : F --> G) (H : ∏ a : ob C, isMonic (pr1 α a)) : isMonic α.
proof: Proof. intros G' β η H'. use (nat_trans_eq). - apply D. - intros x. set (H'' := nat_trans_eq_pointwise H' x). cbn in H''. apply (H x) in H''. exact H''. Qed.
imports: UniMath.Foundations.PartD UniMath.Foundations.Propositions UniMath.Foundations.Sets UniMath.CategoryTheory.Core.Categories UniMath.CategoryTheory.Core.Isos UniMath.CategoryTheory.Core.NaturalTransformations UniMath.CategoryTheory.FunctorCategory UniMath.CategoryTheory.Subcategory.Core UniMath.CategoryTheory.Core.Functors