I believe that a vimeo video is added to a category - determined by vimeo through some intelligent algorithm. The vimeo.videos.getInfo method does not seem to provide the category. Is it possible, through an api call, to retrieve that category to which a specific vimeo video has been added?
/categories/[id]/videos/[id] is a pattern that the Vimeo API often uses for checking whether something exists in something else. Unfortunately it is not currently supported in the API.
I'll make a note to add it in the future.