# Applications of opetopes

I've been reading about coherence problems in homotopy type theory (regarding semisimplicial sets and a raw syntax interpreter), and I've seen a remark about higher-dimensional operads perhaps being the notion which would enable one to encode coherence data into equality (I think they said this about judgemental equality).

So I got to opetopes. I remember reading about some applications of opetopes/opetopic sets outside higher-dimensional category theory (something like biological or social systems, I think), but I have forgotten where it was and haven't been able to find them.

Could someone point me to papers/websites discussing unorthodox applications of opetopes?

I'm doing my final work for IT classes about opetopes, and it could be more interesting if I were able to demonstrate more diverse range of use cases.

Many thanks!

• Is this what you call a dodecahedron in Wisconsin? – Sam Hopkins Oct 16 at 14:19

Opetopes arose long before homotopy type theory, back when mathematicians were trying to find the "right" definition of a weak $$n$$-category. They were invented by Baez and Dolan as part of a research program to model topological quantum field theories using higher category theory. So, stretching the meaning of the word "application" one could say there was an application of opetopes to mathematical physics.
• I would add that Baez & Dolan introduction of opetopes was more precisely in order to give one of the first (I think the first to be published ?) définition of weak $\infty$-categories and $(\infty,n)$-categories. In their papers, Opetopes serve as a combinatorial tool to record higher coherence conditions. – Simon Henry Oct 16 at 16:43