add_rewrite_rule to remove /category/ from permalink

I believe the rewrite rule your wanting to alter is this

category/(.+?)/?$ index.php?category_name=$matches[1] category

to do what you want it should just be a case of adding the following rewrite rule in your functions.php

add_rewrite_rule('(.+?)/?$', 'index.php?category_name=$matches[1]', 'top');

this should work but might conflict with other rules so that will be worth checking.