Is it possible to limit users to adding/editing entries in specific categories?
Entry permissions are sort of an all or nothing thing. If they can publish entries, they can publish all entries or just their own entries. The tricky part of this kind of permission is that Craft doesn't know if a category field will be on a particular entry type.

A possible way to make this work is to create a custom plugin that fires the entries.onBeforeSaveEntry event, and checks each user's category access with the entry's categories. Granted, you run into the issue of them being able to remove the category to remove any problems.

A second option is to give them a special front-end portal area that will let them edit entries, and let you filter those entries to what they can edit. You will also then be able to omit fields that you don't want them to edit (including the categories that prohibit their access).