Yes, you are right.
Part of Yahoo email server is down right now.
You can check the status of Yahoo server athttp://downrightnow.com/yahoomail
In the mean time, please see if you can use the limited web page version:http://us.m.yahoo.com/p/mail
and see if you can check your emails.
This is a temporary service disruption from Yahoo side. Their servers are down at the moment. Not all, but lots of users are facing this now. Don't worry about your email messages, they will be safe.
Please try again tomorrow and you can always check the Yahoo server status at http://downrightnow.com/yahoomail
Please let me know later if there is still any issue. Please let me know how it goes later . Thank you.