Weak n-categories: comparing opetopic foundations

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.

31 pages

References in corpus (2)

• The category of opetopes and the category of opetopic sets
• Weak n-categories: opetopic and multitopic foundations

Cited by in corpus (4)

• The category of opetopes and the category of opetopic sets
• Opetopic bicategories: comparison with the classical theory
• Weak n-categories: opetopic and multitopic foundations
• An alternative characterisation of universal cells in opetopic n-categories