| 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 | |