toEndHom — Mathlib

English

The additive action yields a monoid hom from M to AddEnd(α): toEndHom [AddAction M α] : M →+ AddEnd(α) with toFun m acting as x ↦ m • x.

Русский

Добавитное действие порождает моноид-гомоморфизм из M в AddEnd(α): toEndHom [AddAction M α] : M →+ AddEnd(α) с к делу: toFun m действует как x ↦ m • x.

LaTeX

$$$\mathrm{toEndHom} : M \to_+ \mathrm{AddEnd}(\alpha), \quad \mathrm{toEndHom}(m)(x) = m \cdot x.$$$

Lean4

/-- The monoid hom representing a monoid action.

When `M` is a group, see `MulAction.toPermHom`. -/
def toEndHom [MulAction M α] : M →* Function.End α
    where
  toFun := (· • ·)
  map_one' := funext (one_smul M)
  map_mul' x y := funext (mul_smul x y)

Похожие утверждения