| import OAI.Algebra.Finitistic.Selected.SelectedOrdinaryModules | |
| import OAI.Algebra.Finitistic.Bar.FiniteBarResolution | |
| namespace OAI | |
| noncomputable section | |
| open CategoryTheory | |
| namespace LittleFinitistic.SelectedBarResolution | |
| open SelectedOrdinaryAlgebra SelectedOrdinaryModules | |
| /-- The genuine absolute bar projective resolution of each actual inflated | |
| module. It can have infinitely many nonzero degrees. -/ | |
| def resolution (Y : FiniteSelectionFamily.S.{0}) : ProjectiveResolution (module Y) := | |
| DerivedBar.projectiveResolution ℂ A (Inflated Y) | |
| theorem finite_free (Y : FiniteSelectionFamily.S.{0}) (n : ℕ) : | |
| Module.Finite A ((resolution Y).complex.X n) ∧ | |
| Module.Free A ((resolution Y).complex.X n) := | |
| ⟨DerivedBar.projectiveResolution_finite ℂ A (Inflated Y) n, | |
| DerivedBar.projectiveResolution_free ℂ A (Inflated Y) n⟩ | |
| end LittleFinitistic.SelectedBarResolution | |
| end | |
| end OAI | |