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for completeness (prompted by opetopic type theory) I started an entry opetopic omega-category.
For me presently this just serves to purpose to record Thorsten Palm’s definition of opetopic omega-category, as I understand it from what Eric Finster tells me.
For the definitions by Baez-Dolan and by Makkai the entry presently only contains placeholders, please feel invited to fill in detail.
All these definitions consider opetopic sets. The difference is in which structure and property is put on that. The original definition of universal cells is somewhat involved, as far as I see. Palm’s definition is of a nice straightforward homotopy-theoretic flavor. It seems plausible that this definition satisfies the homotopy hypothesis, but I don’t know if anyone looked into it.
Accoring to Eric Finster, Palm showed that his definition is a special case of Makkai’s, but the converse remains open.
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