| 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 | |