| import OAI.Algebra.AuslanderReiten.Ext.AExtCoefficientCore |
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| namespace OAI |
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| 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 (hq : q ≠ 0) (hq1 : 1+q ≠ 0) (h : NoPositivePowerOne q) |
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|
| abbrev aCoefficientFunction (n : ℕ) := fun x : ASelfExt q (3*n) => |
| tTensorCoefficientEquiv q hq hq1 h n (aExtKunnethEquiv q (3*n) x) |
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|
| theorem aCoefficientFunction_injective (n : ℕ) : |
| Function.Injective (aCoefficientFunction q hq hq1 h n) := |
| (tTensorCoefficientEquiv q hq hq1 h n).injective.comp |
| (aExtKunnethEquiv q (3*n)).injective |
|
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| theorem aCoefficientFunction_surjective (n : ℕ) : |
| Function.Surjective (aCoefficientFunction q hq hq1 h n) := |
| (tTensorCoefficientEquiv q hq hq1 h n).surjective.comp |
| (aExtKunnethEquiv q (3*n)).surjective |
|
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| theorem aCoefficientFunction_add (n : ℕ) (x y : ASelfExt q (3*n)) : |
| type_of% ((congrArg (tTensorCoefficientEquiv q hq hq1 h n) |
| ((aExtKunnethEquiv q (3*n)).map_add x y)).trans |
| ((tTensorCoefficientEquiv q hq hq1 h n).map_add |
| (aExtKunnethEquiv q (3*n) x) (aExtKunnethEquiv q (3*n) y))) := |
| (congrArg (tTensorCoefficientEquiv q hq hq1 h n) |
| ((aExtKunnethEquiv q (3*n)).map_add x y)).trans |
| ((tTensorCoefficientEquiv q hq hq1 h n).map_add |
| (aExtKunnethEquiv q (3*n) x) (aExtKunnethEquiv q (3*n) y)) |
|
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| end ArExplicit.Resolution |
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| end |
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| end OAI |
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|
