| import OAI.Algebra.AuslanderReiten.Ext.AExtCentral | |
| import OAI.Algebra.AuslanderReiten.Bar.ModuleBarTensorCentralAction | |
| 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))] | |
| variable (hq : q ≠ 0) (hq1 : 1+q ≠ 0) (h : NoPositivePowerOne q) | |
| local notation "T" => ArExplicit.T k q | |
| include hq hq1 h | |
| theorem aFirst_kunneth_right (n : ℕ) (x : ASelfExt q (3*n)) : | |
| type_of% (ModuleBar.tensorFirst_action_right k T T (Simple q) (Simple q) | |
| (CocycleData.p q) (CocycleData.p_isCocycle3 q) | |
| (CocycleData.p q) (CocycleData.p_isCocycle3 q) | |
| (tExplicitP q) (aFactorExtClass q) (tExplicitP q) (aFactorExtClass q) | |
| (tTensor_generation q hq hq1 h) (aEndHom_scalar q hq1) n x) := | |
| ModuleBar.tensorFirst_action_right k T T (Simple q) (Simple q) | |
| (CocycleData.p q) (CocycleData.p_isCocycle3 q) | |
| (CocycleData.p q) (CocycleData.p_isCocycle3 q) | |
| (tExplicitP q) (aFactorExtClass q) (tExplicitP q) (aFactorExtClass q) | |
| (tTensor_generation q hq hq1 h) (aEndHom_scalar q hq1) n x | |
| theorem aSecond_kunneth_right (n : ℕ) (x : ASelfExt q (3*n)) : | |
| type_of% (ModuleBar.tensorSecond_action_right k T T (Simple q) (Simple q) | |
| (CocycleData.p q) (CocycleData.p_isCocycle3 q) | |
| (CocycleData.p q) (CocycleData.p_isCocycle3 q) | |
| (tExplicitP q) (aFactorExtClass q) (tExplicitP q) (aFactorExtClass q) | |
| (tTensor_generation q hq hq1 h) (aEndHom_scalar q hq1) n x) := | |
| ModuleBar.tensorSecond_action_right k T T (Simple q) (Simple q) | |
| (CocycleData.p q) (CocycleData.p_isCocycle3 q) | |
| (CocycleData.p q) (CocycleData.p_isCocycle3 q) | |
| (tExplicitP q) (aFactorExtClass q) (tExplicitP q) (aFactorExtClass q) | |
| (tTensor_generation q hq hq1 h) (aEndHom_scalar q hq1) n x | |
| end ArExplicit.Resolution | |
| end | |
| end OAI | |