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2c7d975 | 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 30 31 | 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
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