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216fb31 | 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 | 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
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