instDistribMulActionOfSMulCommClass

English

If S acts on the codomain, then the action distributes through the composition: (s • g).compMultilinearMap f = s • (g.compMultilinearMap f).

Русский

Если S действует на кодомаппинг, то действие распространяется на композицию: (s • g).compMultilinearMap f = s • (g.compMultilinearMap f).

LaTeX

$$$$ (s \cdot g) .compMultilinearMap f = s \cdot (g .compMultilinearMap f). $$$$

Lean4

instance [Monoid S] [DistribMulAction S M₂] [Module R M₂] [SMulCommClass R S M₂] :
    DistribMulAction S (MultilinearMap R M₁ M₂) :=
  coe_injective.distribMulAction coeAddMonoidHom fun _ _ ↦ rfl

Похожие утверждения