Database and Categories

I want to do a lot of recategorising. Rather than ‘Edit post’ over 500 times, I wondered if just altering a number in the database might do the trick …. but looking at an entry in wp_posts, there doesn’t seem to be anything there to indicate a category.
I’m guessing that a post is given a number, and that one of the values given to that number is also the category value. Is that so ?
And has anyone found a nippier way of recat’ing lots of posts ?