| import OAI.Algebra.Finitistic.Bar.IntegerDerivedMultibar | |
| namespace OAI | |
| noncomputable section | |
| open CategoryTheory | |
| namespace DerivedBar | |
| universe u | |
| variable (D : Type u) [Ring D] | |
| local instance : HasDerivedCategory.{u+1} (ModuleCat.{u} D) := | |
| HasDerivedCategory.standard (ModuleCat.{u} D) | |
| /-- The original nonnegative stalk maps to the actual integer derived stalk. -/ | |
| def integerStalkIso (N : ModuleCat.{u} D) : | |
| (integerQ D).obj ((ChainComplex.single₀ (ModuleCat D)).obj N) ≅ | |
| (DerivedCategory.singleFunctor (ModuleCat D) 0).obj N := | |
| DerivedCategory.Q.mapIso (HomologicalComplex.extendSingleIso | |
| ComplexShape.embeddingDownNat N 0 0 rfl) ≪≫ | |
| ((DerivedCategory.singleFunctorIsoCompQ (ModuleCat D) 0).app N).symm | |
| end DerivedBar | |
| end | |
| end OAI | |