# What is [duality-theorem] for?

There are several concepts of duality in mathematics. There is the duality in the sense of category theory, and there is duality in optimization, and there is duality in order theory (which is closer to the one in category theory, I believe).

I don't know too much about these topics, so I can't fully judge that myself. But the tag seems to have questions from all sort of dualities in mathematics. That seems like a particularly bad practice in my eyes, at least if those concepts are "disjoint" or "orthogonal" in some sense.

To drive the point home, consider the tag "regularity" in which every question about objects which can be called "regular" fits. That's an extremely bad tagging philosophy.

Since I don't know too much about duality, I wanted to raise this on meta so someone else could perhaps clarify things and write tag wikis, and then we can decide whether or not this tag needs a thorough cleanup, or maybe removal.

• I think the tag is unsalvageable. Keeping Poincaré duality, linear program duality, and dual Banach spaces under the same tag defies common sense. (Not to mention the categorical stuff, which defies common sense on its own.) I'd say delete the tag. It shall be neither mine nor yours. Jul 18, 2013 at 13:44
• We can also consider removing a cap on the number of tags... then people can search questions of the sort "subject" "duality" "..." which would make the tag useful again Jul 19, 2013 at 18:04
• @frogeyedpeas: Yes, of course. Nothing is better than someone putting pretty much every general purpose tag on a question because they don't know that it's really off topic! :\
– Asaf Karagila Mod
Jul 19, 2013 at 18:11
• Well I was hoping we can assume that people knew how to tag properly Jul 19, 2013 at 20:14
• @frogeyedpeas: If the past is any indication, they don't. Besides, five tags is plenty. I don't see a reason to increase that number. If something is so broad that it literally fits on more than five tags, then perhaps it is too broad for this site.
– Asaf Karagila Mod
Jul 19, 2013 at 20:18
• What about inter subject related questions? Jul 19, 2013 at 20:19
• @frogeyedpeas: These questions have merits, of course, but at some point they become clearly more about one subject than the other. Moreover I can't think of something which is "truly" fitting to five tags, which cannot be covered by an "umbrella tag" (e.g. abstract-algebra is an umbrella tag, with respect to the many many algebra related tags).
– Asaf Karagila Mod
Jul 19, 2013 at 20:28
• I think it is possible that all kinds of dualities are dualities in some common sense. At least when hear the word "duality" in an unknown context, i already guess that probably there is some involution involved, and theorems or formulas will come in pairs. Jul 22, 2013 at 8:28
• @Alexey: This isn't enough to assert the usefulness of the tag. Whenever I hear an object is called "normal" or "regular" I instantly know that it is the prime example of this sort of object. It doesn't mean that [normal-things] is going to be a useful tag.
– Asaf Karagila Mod
Jul 23, 2013 at 7:13