| import OAI.Algebra.AuslanderReiten.Ext.AExtActions | |
| import OAI.Algebra.AuslanderReiten.Bar.ModuleBarTensorProducts | |
| 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 ⊗[k] ArExplicit.T k q))] | |
| local notation "T" => ArExplicit.T k q | |
| theorem aFirst_second_commute : | |
| type_of% (ModuleBar.tensorCubics_commute k T T (Simple q) (Simple q) | |
| (CocycleData.p q) (CocycleData.p_isCocycle3 q) | |
| (CocycleData.p q) (CocycleData.p_isCocycle3 q)) := | |
| ModuleBar.tensorCubics_commute k T T (Simple q) (Simple q) | |
| (CocycleData.p q) (CocycleData.p_isCocycle3 q) | |
| (CocycleData.p q) (CocycleData.p_isCocycle3 q) | |
| end ArExplicit.Resolution | |
| end | |
| end OAI | |