toAlgHomMonoidHom — Mathlib

English

The underlying AlgHom of the product of endomorphisms equals the product of the underlying AlgHoms: AlgHom.from(f₁.prod f₂) = AlgHom.from(f₁) . prod AlgHom.from(f₂).

Русский

Подложный AlgHom произведения эндоморфизмов равен произведению подлежащих AlgHom.

LaTeX

$$AlgHomClass.toAlgHom (f₁.prod f₂) = (AlgHomClass.toAlgHom f₁).prod (AlgHomClass.toAlgHom f₂)$$

Lean4

/-- coercion from `ContinuousAlgHom` to `AlgHom` as a `RingHom`. -/
@[simps]
def toAlgHomMonoidHom : (A →A[R] A) →* A →ₐ[R] A where
  toFun := (↑)
  map_one' := rfl
  map_mul' _ _ := rfl

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