rTensorAlgHom — Mathlib

English

The map lTensorAlgHom is implemented as an algebra homomorphism from End_R(M) to End_R(N ⊗_R M) given by the linear maps lTensorHom and lTensor_mul along with lTensor_id.

Русский

Построение lTensorAlgHom задаёт алгебра-морфизм от End_R(M) к End_R(N ⊗_R M) через линейные отображения lTensorHom и lTensor_mul и единичный тензор.

LaTeX

$$$\\text{lTensorAlgHom} : \\mathrm{End}_R(M) \\to_{\\,\\}^{\\,\\} \\mathrm{End}_R(N \\otimes_R M)$$$

Lean4

/-- The map `LinearMap.rTensorHom` which sends `f ↦ f ⊗ 1` as a morphism of algebras. -/
@[simps!]
def rTensorAlgHom : Module.End R M →ₐ[R] Module.End R (M ⊗[R] N) :=
  .ofLinearMap (rTensorHom (M := N)) (rTensor_id N M) (rTensor_mul N)

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