instMonoid — Mathlib

English

The space of equivariant maps X→ₑ[σ] Y carries a monoid structure under pointwise multiplication of maps.

Русский

Пространство эквивariantных отображений X→ₑ[σ]Y образует моноид под поко̄мовым умножением.

LaTeX

$$$\text{Monoid}(X \to_{\sigma} Y)$ with pointwise multiplication.$$

Lean4

instance [SMul M X] [Monoid N] [Monoid Y] [MulDistribMulAction N Y] : Monoid (X →ₑ[σ] Y)
    where
  mul f g := ⟨f * g, by simp⟩
  mul_assoc _ _ _ := ext fun x ↦ mul_assoc _ _ _
  one := ⟨1, by simp⟩
  one_mul _ := ext fun x ↦ one_mul _
  mul_one _ := ext fun x ↦ mul_one _

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