Theorems · Definition · linear algebra

Finsupp.mapRange.linearEquiv

{α : Type u_1} →
  {M : Type u_2} →
    {N : Type u_3} →
      {R : Type u_5} →
        {R₂ : Type u_6} →
          [inst : Semiring R] →
            [inst_1 : Semiring R₂] →
              [inst_2 : AddCommMonoid M] →
                [inst_3 : Module R M] →
                  [inst_4 : AddCommMonoid N] →
                    [inst_5 : Module R₂ N] →
                      {σ₁₂ : R →+* R₂} →
                        {σ₂₁ : R₂ →+* R} →
                          [inst_6 : RingHomInvPair σ₁₂ σ₂₁] →
                            [inst_7 : RingHomInvPair σ₂₁ σ₁₂] → (M ≃ₛₗ[σ₁₂] N) → (α →₀ M) ≃ₛₗ[σ₁₂] α →₀ N

Finsupp.mapRange as a LinearEquiv.

Defined in

Mathlib.LinearAlgebra.Finsupp.Defs

Cited by

24 results in Mathlib

Foundations

Depth 75 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

SemiringSemiringAddCommMonoidModuleAddCommMonoidModuleRingHomInvPairRingHomInvPair