| import OAI.Algebra.Finitistic.Localization.NativeProjectiveModel | |
| import OAI.Algebra.Finitistic.Bimodule.BimoduleDerivedShift | |
| namespace OAI | |
| noncomputable section | |
| open CategoryTheory | |
| namespace LittleFinitistic.BimoduleTotal.BoundedProjective | |
| open ExternalTensor.Section4 | |
| universe u | |
| variable {k B : Type u} [Field k] [Ring B] [Algebra k B] | |
| variable {P : BiComplex k B} (data : BoundedProjective k B P) | |
| variable [HasDerivedCategory.{u+1} (ModuleCat.{u} B)] | |
| /-- Native degree-zero module embedding, with the module's original compatible scalar action. -/ | |
| def nativeSingleEvaluation (N : Type u) [AddCommGroup N] [Module k N] [Module B N] | |
| [IsScalarTower k B N] : | |
| data.derived.obj ((DerivedCategory.singleFunctor (ModuleCat.{u} B) 0).obj (ModuleCat.of B N)) ≅ | |
| DerivedCategory.Q.obj (((BimoduleBalancedTensor.functor k B N).mapHomologicalComplex (.up ℤ)).obj P) := | |
| data.nativeEvaluation N | |
| end LittleFinitistic.BimoduleTotal.BoundedProjective | |
| end | |
| end OAI | |