| 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 |
| |
