As long as you're getting enough sleep at night after staying up until 2:00 AM then there's nothing wrong with going to sleep at 2:00 AM and waking up at 1:00 PM.
Some nights on weekends I will stay up until 2:00 AM and sometimes as late as 3:00 AM and get up around 1:00 PM to 2:00 PM when I have time to sleep late.
However if you need to be up sooner than 1:00 PM then you should go to bed early enough to get enough sleep before waking up.
A person needs between 8 to 10 hours of sleep per night to get enough rest and be alert the next day and without enough sleep you're not very alert and can make several mistakes and even sometimes it can be deadly.