Theorems · Definition · commutative algebra

LinearEquiv.symm

{R : Type u_1} →
  {S : Type u_6} →
    {M : Type u_7} →
      {M₂ : Type u_9} →
        [inst : Semiring R] →
          [inst_1 : Semiring S] →
            [inst_2 : AddCommMonoid M] →
              [inst_3 : AddCommMonoid M₂] →
                {module_M : Module R M} →
                  {module_S_M₂ : Module S M₂} →
                    {σ : R →+* S} →
                      {σ' : S →+* R} →
                        {re₁ : RingHomInvPair σ σ'} → {re₂ : RingHomInvPair σ' σ} → (M ≃ₛₗ[σ] M₂) → M₂ ≃ₛₗ[σ'] M

Linear equivalences are symmetric.

Defined in

Mathlib.Algebra.Module.Equiv.Defs

Cited by

1,461 results in Mathlib

Foundations

Depth 26 from the axioms, rests on 215 definitions · uses propext, Quot.sound

Assumes

SemiringSemiringAddCommMonoidAddCommMonoid