Theorems · Definition · linear algebra

Module.piEquiv

(ι : Type u_1) →
  (R : Type u_2) →
    (M : Type u_3) →
      [Finite ι] →
        [inst : CommSemiring R] → [inst_1 : AddCommMonoid M] → [inst_2 : Module R M] → (ι → M) ≃ₗ[R] (ι → R) →ₗ[R] M

The natural linear equivalence: Mⁱ ≃ Hom(Rⁱ, M) for an R-module M.

Defined in: Mathlib.LinearAlgebra.StdBasis
Cited by: 3 results in Mathlib
Foundations: Depth 87 from the axioms · uses propext, Classical.choice, Quot.sound
Assumes: Finite CommSemiring AddCommMonoid Module

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Cites9

Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.

Modulestatement and proof · cited by 20,661
RingHom.idstatement · cited by 18,349
AddCommMonoidstatement and proof · cited by 12,281
CommSemiringstatement and proof · cited by 10,911
LinearMapstatement · cited by 10,215
LinearEquivstatement · cited by 3,317
Finitestatement and proof · cited by 3,029
Pi.basisFunproof · cited by 78
Module.Basis.constrproof · cited by 37

Cited by3

Results whose statement or proof uses this declaration.

Module.range_piEquivstatement · cited by 1
Module.surjective_piEquiv_apply_iffstatement · cited by 0
Module.piEquiv_apply_applystatement · cited by 0