Arkham City is a recurring place H. P. Lovecraft's prose - the location of Miskatonic university which hosts the deadly Necronomicon. It is also "famous" for Arkham sanitarium, where end those who had an unfortunate chance to glance at things they shouldn't. But besides these two places, it's a beautiful New England town.
Why then is the infamous psychiatric hospital where maniacs such as Joker or Two-Face spend their time between escapes called the same name? Is it pure coincidence or is there a connection between those two places?