Storing products in multiple, deeply nested category tables.

Image Magic 6.9.2-0
ModSecurity 2.9.0

git 2.5.1

I am developing an e-commerce site with a very dynamic vendor.  They provide an XML datafeed to completely update inventory twice per day and update inventory status every 15 minutes.  The first part of the file is a list of 200+ categories (all parent). I need to convert that to about eight deeply nested (five to six deep in some cases) categories.  An example would be Men's>Accessories>Jewelry>Watches>Sport>Aviator.  Almost all products fall into two categories and some five or six.  What is the best way to set up the tables to support this?  If I have six category fields in my catalogue file there would be a lot of empty fields.  I am thinking about creating different "parent" tables but that would require more joins and I am trying to make this as efficient and fast as possible.  Any suggestions would be greatly appreciated.