Offensive Questions I Can't Help But Ask #1

I'm an insensitive asshole and I'm filled with insensitive asshole questions. I spend a lot of time alone left to my own devices so random questions pop into my head that I have no one to immediately ask. So they fester and boil somewhere in the part of my brain that makes questions. I think there is no better forum then the internet to ask such things because I'm bound to get some sort of response. Here's my first question:

Can cat's have downs syndrome?

The picture above is from mycathatesyou.blogspot.com and was the first thing that appeared on google images when I searched "cats + downs syndrome". Her name is Abigail.