Theorems · Definition · number theory

QuadraticForm.tmul

{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] →
                              QuadraticForm A M₁ → QuadraticForm R M₂ → QuadraticForm A (TensorProduct R M₁ M₂)

The tensor product of two quadratic forms, a shorthand for dot notation.

Defined in

Mathlib.LinearAlgebra.QuadraticForm.TensorProduct

Cited by

33 results in Mathlib

Foundations

Depth 80 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

CommRingCommRingAddCommGroupAddCommGroupAlgebraModuleModuleSMulCommClassIsScalarTowerModuleInvertible