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216fb31 | 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 39 40 41 42 43 44 | import OAI.Algebra.Finitistic.Localization.BoundedQuotientEvaluation
namespace OAI
noncomputable section
open CategoryTheory CategoryTheory.Limits
namespace LittleFinitistic.QuadraticEncoding
open ThickEvaluation
universe u v
variable {k : Type u} [Field k] {d t : ℕ} (P : Relations k d t)
/-- The constructed quotient carries its canonical triangulated structure. -/
theorem boundedQ_triangulated : IsTriangulated (BoundedQ P) := inferInstance
variable {P} {Y : Type v} [AddCommGroup Y] [Module k Y] (X : Representation P Y)
instance quotientEvaluationAdditive : (boundedQuotientEvaluation X).Additive := by
rw [Localization.functor_additive_iff (boundedDenominators P).Q (boundedDenominators P)]
exact Functor.additive_of_iso (boundedQuotientEvaluationFactors X).symm
instance quotientEvaluationLifting : Localization.Lifting
(boundedDenominators P).Q (boundedDenominators P)
(boundedEvaluation X) (boundedQuotientEvaluation X) :=
⟨boundedQuotientEvaluationFactors X⟩
instance quotientEvaluationShift : (boundedQuotientEvaluation X).CommShift ℤ :=
Functor.commShiftOfLocalization (boundedDenominators P).Q (boundedDenominators P) ℤ
(boundedEvaluation X) (boundedQuotientEvaluation X)
instance quotientEvaluationFactorsShift :
NatTrans.CommShift (boundedQuotientEvaluationFactors X).hom ℤ :=
inferInstanceAs (NatTrans.CommShift
(Localization.Lifting.iso (boundedDenominators P).Q (boundedDenominators P)
(boundedEvaluation X) (boundedQuotientEvaluation X)).hom ℤ)
instance quotientEvaluationTriangulated : (boundedQuotientEvaluation X).IsTriangulated := by
have : (boundedDenominators P).Q.mapArrow.EssSurj :=
Localization.essSurj_mapArrow (boundedDenominators P).Q (boundedDenominators P)
exact Functor.isTriangulated_of_precomp_iso (boundedQuotientEvaluationFactors X)
end LittleFinitistic.QuadraticEncoding
end
end OAI
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