Theorems · Definition · linear algebra

DFinsupp.lsum

{ι : Type u_1} →
  {R : Type u_3} →
    (S : Type u_4) →
      {M : ι → Type u_5} →
        {N : Type u_6} →
          [inst : Semiring R] →
            [inst_1 : (i : ι) → AddCommMonoid (M i)] →
              [inst_2 : (i : ι) → Module R (M i)] →
                [inst_3 : AddCommMonoid N] →
                  [inst_4 : Module R N] →
                    [DecidableEq ι] →
                      [inst_6 : Semiring S] →
                        [inst_7 : Module S N] →
                          [inst_8 : SMulCommClass R S N] → ((i : ι) → M i →ₗ[R] N) ≃ₗ[S] (Π₀ (i : ι), M i) →ₗ[R] N

The DFinsupp version of Finsupp.lsum. See note [bundled maps over different rings] for why separate R and S semirings are used.

Defined in

Mathlib.LinearAlgebra.DFinsupp

Cited by

21 results in Mathlib

Foundations

Depth 85 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

SemiringAddCommMonoidModuleAddCommMonoidModuleDecidableEqSemiringModuleSMulCommClass