| import Mathlib | |
| open CategoryTheory | |
| variable {C D : Type*} [Category C] [Category D] | |
| theorem karoubi_universal_property [IsIdempotentComplete D] (F : C ⥤ D) : | |
| ∃ (F' : Idempotents.Karoubi C ⥤ D), Nonempty ((Idempotents.toKaroubi C) ⋙ F' ≅ F) := by | |
| sorry | |
| theorem karoubi_universal_property_unique_up_to_iso [IsIdempotentComplete D] {F : C ⥤ D} | |
| {F₁ F₂ : Idempotents.Karoubi C ⥤ D} | |
| (h₁ : Nonempty ((Idempotents.toKaroubi C) ⋙ F₁ ≅ F)) | |
| (h₂ : Nonempty ((Idempotents.toKaroubi C) ⋙ F₂ ≅ F)) : | |
| Nonempty (F₁ ≅ F₂) := by | |
| sorry | |