Theorems · Definition · linear algebra

LinearEquiv.prodComm

(R : Type u_3) →
  (M : Type u_4) →
    (N : Type u_5) →
      [inst : Semiring R] →
        [inst_1 : AddCommMonoid M] →
          [inst_2 : AddCommMonoid N] → [inst_3 : Module R M] → [inst_4 : Module R N] → (M × N) ≃ₗ[R] N × M

Product of modules is commutative up to linear isomorphism.

Defined in

Mathlib.LinearAlgebra.Prod

Cited by

17 results in Mathlib

Foundations

Depth 21 from the axioms · uses propext, Quot.sound

Assumes

SemiringAddCommMonoidAddCommMonoidModuleModule