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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 | import OAI.Algebra.Finitistic.Localization.QuotientActionEvaluation
namespace OAI
noncomputable section
open CategoryTheory
namespace LittleFinitistic
open BalancedTensor FiniteProjectiveHomotopy
universe u v w z
namespace BalancedTensor
variable (k : Type u) [Field k] (A : Type v) [Ring A] [Algebra k A]
variable (N : Type z) [AddCommGroup N] [Module k N] [Module A N]
instance tensorFunctorLinear : (tensorFunctor.{u,v,w,z} k A N).Linear k where
map_smul {M M'} f c := by
apply ModuleCat.hom_ext
apply BalancedTensor.ext
intro m n
exact LinearMap.congr_fun ((mk k A (ScalarModule k A M') N).map_smul c (f.hom m)) n
instance homotopyEvaluationLinear : (homotopyEvaluation.{u,v,w,z} k A N).Linear k :=
inferInstanceAs (((tensorFunctor.{u,v,w,z} k A N).mapHomotopyCategory (.up ℤ)).Linear k)
end BalancedTensor
namespace QuadraticEncoding
variable {k : Type u} [Field k] {d t : ℕ} {P : Relations k d t}
variable {Y : Type v} [AddCommGroup Y] [Module k Y] (X : Representation P Y)
instance boundedEvaluationLinear : (boundedEvaluation X).Linear k :=
inferInstanceAs ((inclusion (B P)ᵐᵒᵖ ⋙ homotopyEvaluation k (B P) X.Evaluation).Linear k)
instance boundedQuotientEvaluationLinear : (boundedQuotientEvaluation X).Linear k :=
(Localization.functor_linear_iff (boundedDenominators P).Q (boundedDenominators P) k
(boundedEvaluation X) (boundedQuotientEvaluation X)).mp inferInstance
end QuadraticEncoding
end LittleFinitistic
end
end OAI
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