From a clean database, install the Accounting and Finance application. This will indirectly install the product module, which creates menus to create and edit products and product categories. Products can be edited and created, but product categories not. When attempting to edit the automatically created "All Products" category in the web interface, all the fields in the form are read-only. Attempting to create a new product category presents a form with all the input fields disabled.
I know from my testing that installing more modules will make this go away, but I haven't yet determined exactly which ones. I'm guessing that the product module creates the necessary menus and models, but the necessary ACLs to enable users to modify product categories live elsewhere.
I'm using a recent nightly build of 6.1 from the Debian packages provided on openerp.com. Dpkg reports version 6.1-20121130-002722-1, installed on Debian Squeeze.
So, I found that the "stock" module seems to be what has been giving me access to change product categories. Specifically, being in the warehouse management group.
However, without "stock" installed (just accounting), it's the sales manager group that gives me access to edit products. However, it doesn't give access to edit product categories, which doesn't make much sense to me. I went to Settings -> Groups -> Sales Management / Manager -> Edit -> Access Rights -> Create and added full access for product categories, and this is the behavior I'd expect by default. It doesn't make much sense to be able to edit products but not categories.