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d7f9a33 | 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 | import OAI.Algebra.AuslanderReiten.Ext.AExtPolynomial
import OAI.Algebra.AuslanderReiten.Ext.TTensorActions
import OAI.Algebra.AuslanderReiten.Ext.TTensorIdentity
import OAI.Algebra.AuslanderReiten.Ext.ExtKunnethIdentity
import OAI.Algebra.AuslanderReiten.Tensor.ExternalTensorScalarProducts
namespace OAI
noncomputable section
open CategoryTheory CategoryTheory.Abelian
open scoped TensorProduct ModuleCat.Algebra
namespace ArExplicit.Resolution
universe u
variable {k : Type u} [Field k] [CharP k 2] (q : k)
variable [HasDerivedCategory (ModuleCat.{u} (ArExplicit.T k q))]
variable [HasDerivedCategory (ModuleCat.{u} (ArExplicit.T k q ⊗[k] ArExplicit.T k q))]
local notation "T" => ArExplicit.T k q
local notation "S" => ModuleCat.of T (Simple q)
attribute [local instance] moduleCatBaseModule moduleCatBaseTower
theorem aExtKunneth_identity :
type_of% (ModuleBar.tensorKunneth_identity k T T (Simple q) (Simple q)) :=
ModuleBar.tensorKunneth_identity k T T (Simple q) (Simple q)
variable (hq : q ≠ 0) (hq1 : 1+q ≠ 0) (h : NoPositivePowerOne q)
theorem aExtCoefficient_identity :
type_of% ((congrArg (tTensorCoefficientEquiv q hq hq1 h 0)
(aExtKunneth_identity q)).trans (tTensorCoefficient_identity q hq hq1 h)) :=
(congrArg (tTensorCoefficientEquiv q hq hq1 h 0)
(aExtKunneth_identity q)).trans (tTensorCoefficient_identity q hq hq1 h)
end ArExplicit.Resolution
end
end OAI
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