My fur is not to blame for your allergies
Well, technically, it really isn't.
In fact, what makes many people allergic to cats is a protein present in their skin, known as Fel d 1. Some cats produce more than others, but all of them produce it to some extent.
Females produce less than males, and males' levels lower if they're sterilized.
However, removing carpets from your house, washing the cat's bed often, and carefully cleaning surfaces helps to decrease the presence of this protein at home (and therefore decrease allergic reactions).