tensorDistrib — Mathlib

English

The inverse of tensorLId applied to x equals the inverse of TensorProduct.lid applied to x.

Русский

Обратное к tensorLId применимо к x равно обратному TensorProduct.lid применению к x.

LaTeX

$$$(tensorLId Q_2).symm x = (TensorProduct.lid\\, R\\, M_2).symm x$$$

Lean4

/-- The tensor product of two quadratic forms injects into quadratic forms on tensor products.

Note this is heterobasic; the quadratic form on the left can take values in a larger ring than
the one on the right. -/
def tensorDistrib : QuadraticForm A M₁ ⊗[R] QuadraticForm R M₂ →ₗ[A] QuadraticForm A (M₁ ⊗[R] M₂) :=
  (AlgebraTensorModule.rid R A A).congrQuadraticMap.toLinearMap ∘ₗ QuadraticMap.tensorDistrib R A

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