Storing products in multiple, deeply nested category tables.

I apologize but I am truly a noob with Postgresql.

I am using the following platform~

Apache 2.4.18
Postgresql 9.4.6-1
PHP 7.0.4
PHPPgAdmin 5.1
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.