Replying to pbruin:
Is it clear that the "structure category" terminology is the way to go? Personally I still don't like it very much (again, it pretends to be about categories but instead is about relations to their supercategories).
It's more of there has been no better alternative proposed. If we move away from the terminology "structure category", then I feel like we loose the ability to name methods like all_structure_super_categories. However I do understand your objection.
I would prefer the proposals made by Nicolas in comment:9 and Simon in comment:10 to have an additional_structure() method that returns something meaningful about the additional structure, not just True or False.
Currently the default is that new subcategories are structure categories (so they are not full subcategories). If we were to go with returning pairs (op, method), then the question becomes do we want the default to be False or do we allow True to remain the default and have it be when we can't adequately define the structure?
Actually, that made me have a thought. How about instead of is_structure_category we have has_additional_structure, and then we could extend this to additional_structure (on a followup ticket).
