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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 | import OAI.Algebra.Finitistic.Localization.TensorEvaluationFunctor
import Mathlib.Algebra.Category.ModuleCat.Abelian
import Mathlib.Algebra.Homology.HomotopyCategory.Pretriangulated
namespace OAI
noncomputable section
open CategoryTheory
namespace LittleFinitistic.BalancedTensor
universe u v w z
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]
/-- Termwise tensor evaluation on actual complexes, descended through chain homotopies. -/
def homotopyEvaluation :
HomotopyCategory (ModuleCat.{w} Aᵐᵒᵖ) (ComplexShape.up ℤ) ⥤
HomotopyCategory (ModuleCat.{max w z} k) (ComplexShape.up ℤ) :=
(tensorFunctor k A N).mapHomotopyCategory (ComplexShape.up ℤ)
instance homotopyEvaluationShift : (homotopyEvaluation.{u,v,w,z} k A N).CommShift ℤ :=
inferInstanceAs (((tensorFunctor.{u,v,w,z} k A N).mapHomotopyCategory (ComplexShape.up ℤ)).CommShift ℤ)
instance homotopyEvaluationTriangulated : (homotopyEvaluation.{u,v,w,z} k A N).IsTriangulated :=
inferInstanceAs (((tensorFunctor.{u,v,w,z} k A N).mapHomotopyCategory (ComplexShape.up ℤ)).IsTriangulated)
end LittleFinitistic.BalancedTensor
end
end OAI
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