Edit Category of image attachments

All image attachements (and more specifically, their ?attachement_id= subpage that is reached when clicking on a [gallery] entry) get the default category instead of inheriting the same category as the parent post. Ideally, I’d even like to give them their own category.

Is there any way to edit the Category for these ?attachement_id pages? Currently, I have to change the entry right in the MySQL database, which is a hacky and cumbersome way of dealing with this.