Theorems · Definition · number theory

QuadraticForm.tensorDistrib

(R : Type uR) →
  (A : Type uA) →
    {M₁ : Type uM₁} →
      {M₂ : Type uM₂} →
        [inst : CommRing R] →
          [inst_1 : CommRing A] →
            [inst_2 : AddCommGroup M₁] →
              [inst_3 : AddCommGroup M₂] →
                [inst_4 : Algebra R A] →
                  [inst_5 : Module R M₁] →
                    [inst_6 : Module A M₁] →
                      [inst_7 : SMulCommClass R A M₁] →
                        [IsScalarTower R A M₁] →
                          [inst_9 : Module R M₂] →
                            [Invertible 2] →
                              TensorProduct R (QuadraticForm A M₁) (QuadraticForm R M₂) →ₗ[A]
                                QuadraticForm A (TensorProduct R M₁ M₂)

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.

Defined in

Mathlib.LinearAlgebra.QuadraticForm.TensorProduct

Cited by

1 results in Mathlib

Foundations

Depth 79 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

CommRingCommRingAddCommGroupAddCommGroupAlgebraModuleModuleSMulCommClassIsScalarTowerModuleInvertible