There seems to be a disparity between administration levels in our installation of Expression Engine (build 20070815).
If a user goes to Admin › Weblog Administration › Category Groups › Category Management they are able to successfully create a new category for a given weblog. However, if they go to Publish › {weblog} › Categories, then click on the ‘Edit Categories’ link, the resulting popup window indicates the following: “You are not authorized to access this page”.
I believe this may be a bug in the site duplication code (we are running the MSM), as users are able to edit categories via both methods in the site we used as a template for other sites.
I checked the Member Group privileges for the associated Member Group, and can verify that the members have ‘Can edit and add new categories’ and ‘Can delete categories’ set to ‘Yes’.