Theorems · Definition · linear algebra

AlternatingMap.domLCongr

(R : Type u_1) →
  [inst : Semiring R] →
    {M : Type u_2} →
      [inst_1 : AddCommMonoid M] →
        [inst_2 : Module R M] →
          (N : Type u_3) →
            [inst_3 : AddCommMonoid N] →
              [inst_4 : Module R N] →
                (ι : Type u_7) →
                  {M₂ : Type u_10} →
                    [inst_5 : AddCommMonoid M₂] →
                      [inst_6 : Module R M₂] →
                        (S : Type u_12) →
                          [inst_7 : Semiring S] →
                            [inst_8 : Module S N] →
                              [inst_9 : SMulCommClass R S N] → (M ≃ₗ[R] M₂) → M [⋀^ι]→ₗ[R] N ≃ₗ[S] M₂ [⋀^ι]→ₗ[R] N

Construct a linear equivalence between maps from a linear equivalence between domains. This is AlternatingMap.compLinearMap as an isomorphism, and the alternating version of LinearEquiv.multilinearMapCongrLeft. It could also have been called LinearEquiv.alternatingMapCongrLeft.

Defined in

Mathlib.LinearAlgebra.Alternating.Basic

Cited by

6 results in Mathlib

Foundations

Depth 34 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

SemiringAddCommMonoidModuleAddCommMonoidModuleAddCommMonoidModuleSemiringModuleSMulCommClass