| import Mathlib | |
| open CategoryTheory Functor | |
| theorem mono_iff_exists_embedding_section | |
| {C : Type u} [Category.{v} C] {X Y : C} (f : X ⟶ Y) : | |
| Mono f ↔ ∃ (D : Type (max u v)) (_ : Category.{v} D) (I : C ⥤ D) (_ : Faithful I), | |
| IsSplitMono (I.map f) := by | |
| sorry | |