My cat sleeps whenever he's tired or when I go to sleep. He's a proximity cat, so he'll be snoozing nearby depending on where in the house I am. If I go to bed, he's going to go to bed too.
He also doesn't wake me up. The auto feeder gets him food, so I can stay asleep without having to worry about him getting fed. Usually when I wake up he'll be in the mini cat tree or under the bed.