| import Mathlib | |
| open CategoryTheory Functor | |
| universe u v | |
| namespace CategoryTheory | |
| open Category Adjunction | |
| variable {C : Type u₁} {D : Type u₂} {E : Type u₃} | |
| variable [Category.{v₁} C] [Category.{v₂} D] [Category.{v₃} E] | |
| class Reflective2 (R : D ⥤ C) extends R.Faithful where | |
| L : C ⥤ D | |
| adj : L ⊣ R | |
| end CategoryTheory | |
| theorem exists_not_reflective : | |
| ∃ (E C D : Type u) | |
| (_ : Category.{v} E) (_ : Category.{v} C) (_ : Category.{v} D) (i : C ⥤ D) | |
| (_ : Faithful i) (j : D ⥤ E) (_ : Faithful j), | |
| IsEmpty (Reflective2 i) ∧ Nonempty (Reflective2 (i ⋙ j)) := by | |
| sorry | |