Hi,
It seems a very good ideea to show in a module the current item's category description. I mean when you browse a category or an item from a category, to have the description of that category in a module, instead of showing it on content page on top of the item(s).
this way the content can be made more flexible and the relevant information about that item(s) can be displayed in a custom position instead of showing it in content area.
there are a few extensions to show the list of categories in a module but not the description, only the titles. And are not associated with the current items. Same for the authors.