Theorems · Definition · linear algebra

TensorProduct.AlgebraTensorModule.congr

{R : Type uR} →
  {A : Type uA} →
    {M : Type uM} →
      {N : Type uN} →
        {P : Type uP} →
          {Q : Type uQ} →
            [inst : CommSemiring R] →
              [inst_1 : Semiring A] →
                [inst_2 : Algebra R A] →
                  [inst_3 : AddCommMonoid M] →
                    [inst_4 : Module R M] →
                      [inst_5 : Module A M] →
                        [inst_6 : IsScalarTower R A M] →
                          [inst_7 : AddCommMonoid N] →
                            [inst_8 : Module R N] →
                              [inst_9 : AddCommMonoid P] →
                                [inst_10 : Module R P] →
                                  [inst_11 : Module A P] →
                                    [inst_12 : IsScalarTower R A P] →
                                      [inst_13 : AddCommMonoid Q] →
                                        [inst_14 : Module R Q] →
                                          (M ≃ₗ[A] P) → (N ≃ₗ[R] Q) → TensorProduct R M N ≃ₗ[A] TensorProduct R P Q

Heterobasic version of TensorProduct.congr

Defined in

Mathlib.LinearAlgebra.TensorProduct.Tower

Cited by

29 results in Mathlib

Foundations

Depth 73 from the axioms · uses propext, Quot.sound

Assumes

CommSemiringSemiringAlgebraAddCommMonoidModuleModuleIsScalarTowerAddCommMonoidModuleAddCommMonoidModuleModuleIsScalarTowerAddCommMonoidModule