Theorems · Definition · linear algebra

LinearMap.prodOfFinsuppNat

{R : Type u_1} →
  {M : Type u_2} →
    {P : Type u_4} →
      [inst : Semiring R] →
        [inst_1 : AddCommMonoid M] →
          [inst_2 : Module R M] →
            [inst_3 : AddCommMonoid P] → [inst_4 : Module R P] → (P × M →ₗ[R] M) → (ℕ →₀ P) →ₗ[R] P × M

A linear map from a product module P × M to M induces a linear map from P^(ℕ) to M, where the nth component is given by P —ι₁→ P × M composed with P × M —f→ M —ι₂→ P × M n times.

Defined in

Mathlib.LinearAlgebra.Finsupp.Pi

Cited by

4 results in Mathlib

Foundations

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

Assumes

SemiringAddCommMonoidModuleAddCommMonoidModule