| import OAI.Algebra.AuslanderReiten.Tensor.BalancedTensorNativeEvaluation | |
| namespace OAI | |
| noncomputable section | |
| open CategoryTheory | |
| namespace ArExplicit.BalancedTensor | |
| universe u | |
| variable {k R S F : Type u} [Field k] [Ring R] [Ring S] [Algebra k R] | |
| variable [AddCommGroup F] [Module k F] [Module Rᵐᵒᵖ F] [Module S F] | |
| variable [SMulCommClass k S F] [SMulCommClass S Rᵐᵒᵖ F] | |
| variable (M : ModuleCat.{u} R) (N : ModuleCat.{u} S) | |
| theorem functorIso_ext | |
| (d e : (functor (k := k) (R := R) (S := S) (F := F)).obj M ≅ N) | |
| (h : ∀ (f : F) (m : M), | |
| d.hom.hom (letI := moduleCatBaseModule (k := k) (R := R) M; tmul f m) = | |
| e.hom.hom (letI := moduleCatBaseModule (k := k) (R := R) M; tmul f m)) : d = e := by | |
| apply Iso.ext | |
| apply ModuleCat.hom_ext | |
| let := moduleCatBaseModule (k := k) (R := R) M | |
| let := moduleCatBaseTower (k := k) (R := R) M | |
| apply leftHom_ext | |
| exact h | |
| end ArExplicit.BalancedTensor | |
| end | |
| end OAI | |