toLinearMap — Mathlib

English

An integer action is defined to be compatible with the SMul structure on M and M2 when S is a semiring.

Русский

Целочисленная скалярация согласована со структурой SMul на M и M2 при наличии полупринятого кольца S.

LaTeX

$$$\text{CompatibleSMul intModule}$$$

Lean4

/-- `g : R →+* S` is `R`-linear when the module structure on `S` is `Module.compHom S g` . -/
@[simps]
def toLinearMap {R S : Type*} [Semiring R] [Semiring S] (g : R →+* S) :
    letI := compHom S g;
    R →ₗ[R] S :=
  letI := compHom S g
  { toFun := (g : R → S)
    map_add' := g.map_add
    map_smul' := g.map_mul }

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