I'm not sure what the associated crossover would be called, but the Joker is quite obviously an avatar, manifestation, Servitor, or at the very least great triumph of the Word of Dark Humor.
I find it bewoggling that, at least according to a perfunctory Google search on some obvious terms, no one seems to have ever done anything with this self-evident possibility.
I find it bewoggling that, at least according to a perfunctory Google search on some obvious terms, no one seems to have ever done anything with this self-evident possibility.