| import Mathlib | |
| import OAI.Algebra.Finitistic.Basic | |
| namespace OAI | |
| noncomputable section | |
| open CategoryTheory | |
| namespace LittleFinitistic | |
| universe u | |
| variable (A : Type u) [Ring A] | |
| def bigFinitisticDimension : WithBot ℕ∞ := | |
| ⨆ (M : ModuleCat.{u} A) (_ : projectiveDimension M < ⊤), projectiveDimension M | |
| def InjectivesGenerate : Prop := | |
| letI := HasDerivedCategory.standard (ModuleCat.{u} A) | |
| ∀ (P : ObjectProperty (DerivedCategory (ModuleCat.{u} A))), | |
| P.IsClosedUnderIsomorphisms → P.IsTriangulated → | |
| (∀ I : Type u, P.IsClosedUnderColimitsOfShape (Discrete I)) → | |
| (∀ (M : ModuleCat.{u} A), Injective M → | |
| P ((DerivedCategory.singleFunctor (ModuleCat.{u} A) 0).obj M)) → | |
| ∀ X, P X | |
| end LittleFinitistic | |
| end | |
| end OAI | |