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Weak n-categories: comparing opetopic foundations

Eugenia Cheng
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Abstract

We define the category of tidy symmetric multicategories. We construct for each tidy symmetric multicategory Q a cartesian monad (E_Q,T_Q) and extend this assignation to a functor. We exhibit a relationship between the slice construction on symmetric multicategories, and the `free operad' monad construction on suitable monads. We use this to give an explicit description of the relationship between Baez-Dolan and Leinster opetopes.

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Eugenia Cheng. 2003-04-21. Weak n-categories: comparing opetopic foundations. https://arxiv.org/abs/math/0304279

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