Theorems · Definition · linear algebra

LinearEquiv.multilinearMapCongrLeft

{R : Type uR} →
  {ι : Type uι} →
    {M₁ : ι → Type v₁} →
      {M₁' : ι → Type v₁'} →
        {M₂ : Type v₂} →
          [inst : CommSemiring R] →
            [inst_1 : (i : ι) → AddCommMonoid (M₁ i)] →
              [inst_2 : AddCommMonoid M₂] →
                [inst_3 : (i : ι) → Module R (M₁ i)] →
                  [inst_4 : Module R M₂] →
                    [inst_5 : (i : ι) → AddCommMonoid (M₁' i)] →
                      [inst_6 : (i : ι) → Module R (M₁' i)] →
                        ((i : ι) → M₁ i ≃ₗ[R] M₁' i) → MultilinearMap R M₁' M₂ ≃ₗ[R] MultilinearMap R M₁ M₂

An isomorphism of multilinear maps given an isomorphism between their domains. This is MultilinearMap.compLinearMap as a linear equivalence, and the multilinear version of LinearEquiv.congrLeft.

Defined in

Mathlib.LinearAlgebra.Multilinear.Basic

Cited by

5 results in Mathlib

Foundations

Depth 38 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

CommSemiringAddCommMonoidAddCommMonoidModuleModuleAddCommMonoidModule