MathOverflow is a question and answer site for professional mathematicians. Join them; it only takes a minute:

Sign up
Here's how it works:
  1. Anybody can ask a question
  2. Anybody can answer
  3. The best answers are voted up and rise to the top

To my shame I have to admit that I have as yet not looked much into opetopes and opetopic sets.

I am in the process of writing nLab entries on dendroidal sets and noticed that some remarks on the relation to opetopic sets should probably be in order.

Now, I know that I should just sit down and read the opetopic literature. But while I am busy doing that, and since the model structure on dendroidal sets wasn't around when most of it was written: does anyone know more about the relation?

share|cite|improve this question

Urs, do you have a reason to think that there'll be much to say about this? I can see that opetopic and dendroidal sets are both presheaf categories that arise in higher-dimensional category theory. I can see that in both cases, the small category on which you're taking presheaves has a graphical or geometric interpretation, and there are some "face maps", and there's something tree-like going on. But beyond that, I don't see what there is to say. Do you have something in mind?

I just looked in Ittay Weiss's thesis, Dendroidal Sets. "Opetope" is not in the index, nor is the relevant Baez--Dolan paper (Higher Dimensional Algebra III) cited. So I guess he had no thoughts on the matter.

share|cite|improve this answer
I tried to figure out whether opetopic objects are equivalent to dendroidal objects, or if maybe one is a special case of the other. I gave up just because I did not (yet) find a concise, explicit description of the opetopic base category. – Greg Kuperberg Nov 18 '09 at 5:45
Yes, defining the category of opetopes (the presheaves on which are the opetopic sets) is no easy task. Defining the objects seems appreciably easier; it's the maps that make it hard. – Tom Leinster Nov 18 '09 at 6:49
Tom, no, this was just a naive question. You might read it in part as asking "Can anyone give me a better idea of what opetopic sets are like?" I was hoping that the answer would have been that opetopic sets are somehow a vast generalization of dendroidal sets. That would have given me motivation to look into them more closely. But if you say there is no non-superficial relation, I'll take your word for it. Thanks. – Urs Schreiber Nov 18 '09 at 7:45
Greg, thanks for this comment. Even though a negative "result", that's useful to know. – Urs Schreiber Nov 18 '09 at 7:48
Well, I don't say there is no non-superficial relation - just that after a few minutes' thought, I can't see one. That doesn't mean much! – Tom Leinster Nov 18 '09 at 9:02

Your Answer


By posting your answer, you agree to the privacy policy and terms of service.

Not the answer you're looking for? Browse other questions tagged or ask your own question.