Do you let cats sleep in your bed?

So a cat will always be "half asleep" with the ability to always get out of the way when you are able to crash on the top of them? That sounds like they aren't even sleeping. Don't they ever sleep for real? lol

By the way, are your cats having some kind of regular sleeping schedule? I know all animals in cat family are usually more active at night. Not sure about the domesticated ones. Then again, they don't have to go to work, so they can sleep any time they want.