English
If F is a class of maps A → B which are both monoid homomorphisms and continuous, then each f ∈ F yields a continuous monoid hom from A to B by forgetting extra structure.
Русский
Если F — класс отображений A→B, являющихся моноид-гомоморфизмами и непрерывными, то любой элемент f ∈ F дает непрерывный моноид-гомоморфизм A→B через приведение к соответствующей форме.
LaTeX
$$$\mathrm{ofClass}(F)(f) = \mathrm{toContinuousMonoidHom}(f)\in \mathrm{ContinuousMonoidHom}(A,B).$$$
Lean4
/-- For `f : F` where `F` is a class of continuous monoid hom, this yields an element
`ContinuousMonoidHom A B`. -/
@[to_additive /-- For `f : F` where `F` is a class of continuous additive monoid hom, this yields
an element `ContinuousAddMonoidHom A B`. -/
]
def ofClass (F : Type*) [FunLike F A B] [ContinuousMapClass F A B] [MonoidHomClass F A B] (f : F) :
(ContinuousMonoidHom A B) :=
toContinuousMonoidHom f
