I have installed the zAlive theme onto my domain, and it has four tabs at the top on a slidebar. I was wanting to have these tabs in the slidebar, be linked to my different categories, but I'm not sure how to do this. My hopes are to have it so that as you select different tabs from the slidebar, the corresponding posts in each category with show underneath. Any help on this would be appreciated.
While you may not be able to integrate your categories list directly into the slider (this is dependent on how the slider is set up and I haven't used this particular theme), it's possible to display a list of categories and their links that functions in the way you've asked and then apply the same (or similar) styles the slider's tabs use to your categories links. Again, this wouldn't interact with the slider at all, merely mimic its look.
To get a list of categories, you would need to call
Hope this gets you headed in the right direction.