Theorems · Definition · linear algebra

Finsupp.lift

(M : Type u_2) →
  (R : Type u_5) →
    [inst : Semiring R] →
      [inst_1 : AddCommMonoid M] → [inst_2 : Module R M] → (X : Type u_9) → (X → M) ≃+ ((X →₀ R) →ₗ[R] M)

A slight rearrangement from lsum gives us the bijection underlying the free-forgetful adjunction for R-modules.

Defined in

Mathlib.LinearAlgebra.Finsupp.LSum

Cited by

9 results in Mathlib

Foundations

Depth 77 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

SemiringAddCommMonoidModule