Sub domains question…

Hi.

I’d like to create an adult portal.
The domain is registered, it’s hosted, WordPress is installed and it’s working.

But problem, I have a lot of categories.
So i’d like to create sub domains in order to split my blog and make it easier to browse.

for now i’d like to keep the same theme for all my sub domains, but i need the categories to be different and independant from 1 sub domain to another.

So how can i do that ?
Do I have to install the theme one more time for each sub domain ?

Thanks.