Good cat!
(except that it potentially brought the diseases into your home)
Pigeons are filthy disease-filled flying rats. I'm not kidding..
You could risk your health.
Here are some of your new potential flat-mates
Pigeon ticks (Argas reflexus)
http://www.jcehrlich.com/pest-guides...s/pigeon-tick/
(very resistent dangerous bugs that can hibernate up to 5 years)
http://www.jacionline.org/article/S0...052-X/abstract
Bed bugs
http://www.pestproducts.com/bedbug.htm
Pigeon fleas infesting humans
http://www.radoslawspiewak.net/2004-5.htm
Pigeons are not cute...
Good luck
