arrowMulDistribMulAction — Mathlib

English

ArrowAction (A → M) carries a MulDistribMulAction structure when M is a monoid: smul on arrows respects one and multiplication pointwise.

Русский

Структура ArrowAction для функций A → M образует MulDistribMulAction, если M моноид; действие на константы и произведения действует по точечному правилу.

LaTeX

$$$ \text{arrowMulDistribMulAction} : MulDistribMulAction G (A \to M)$ with laws $\text{smul_one}$ and $\text{smul_mul}$$$

Lean4

/-- When `M` is a monoid, `ArrowAction` is additionally a `MulDistribMulAction`. -/
def arrowMulDistribMulAction : MulDistribMulAction G (A → M)
    where
  smul_one _ := rfl
  smul_mul _ _ _ := rfl

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