I have a couple of cats at home.  They're pretty funny.
I agree, are they typically furry, carnivorous mammals? 
Yes, although they mainly eat cat food.  They have intense chases around the yard.
Do you value them for companionship or for their ability to hunt vermin?.
A little of both.  They do like to chase birds away.  But when they're done playing they rub up on me all the time, which is nice.
There are more than seventy cat breeds so which ones do you have?