English
The restriction map respects linear structure and coordinates, yielding a multilinear map into the submodule with the same action on inputs.
Русский
Ограничение кодомодуля сохраняет линейную структуру и координаты, образуя мультиленейную карту в подмодуль с тем же действием на входах.
LaTeX
$$toFun = f, map_update_add' and map_update_smul' preserved$$
Lean4
/-- Reinterpret an `A`-multilinear map as an `R`-multilinear map, if `A` is an algebra over `R`
and their actions on all involved modules agree with the action of `R` on `A`. -/
def restrictScalars (f : MultilinearMap A M₁ M₂) : MultilinearMap R M₁ M₂
where
toFun := f
map_update_add' := f.map_update_add
map_update_smul' m i := (f.toLinearMap m i).map_smul_of_tower