Theorems · Definition · commutative algebra

LinearEquiv.lTensor

{R : Type u_1} →
  [inst : CommSemiring R] →
    (M : Type u_7) →
      {N : Type u_8} →
        {P : Type u_9} →
          [inst_1 : AddCommMonoid M] →
            [inst_2 : AddCommMonoid N] →
              [inst_3 : AddCommMonoid P] →
                [inst_4 : Module R M] →
                  [inst_5 : Module R N] →
                    [inst_6 : Module R P] → (N ≃ₗ[R] P) → TensorProduct R M N ≃ₗ[R] TensorProduct R M P

LinearEquiv.lTensor M f : M ⊗ N ≃ₗ M ⊗ P is the natural linear equivalence induced by f : N ≃ₗ P.

Defined in

Mathlib.LinearAlgebra.TensorProduct.Map

Cited by

32 results in Mathlib

Foundations

Depth 62 from the axioms · uses propext, Quot.sound

Assumes

CommSemiringAddCommMonoidAddCommMonoidAddCommMonoidModuleModuleModule