Using a variable to pull posts from category

Where are you trying to use this? What template?

Related:

Stepping Into Templates
Template Hierarchy

But where you want to use that variable? On your main blog page? Or in a [{Category Templates|Category Template]], or a date based archive, or a single post view?

Please review Template Hierarchy if necessary. You will also want to review Stepping Into Template Tags and Stepping Into Templates if you are going to modify a theme to do ‘things’.

You do understand that WordPress automatically will provide you access to category type archives if you assign categories to posts?

If you are talking about a date based archive, then how is that dynamic category variable discovered?

Oh well, probably not understanding you so will point you to Category Templates.