Weak n-categories: opetopic and multitopic foundations

Abstract

We generalise the concepts introduced by Baez and Dolan to define opetopes constructed from symmetric operads with a category, rather than a set, of objects. We describe the category of 1-level generalised multicategories, a special case of the concept introduced by Hermida, Makkai and Power, and exhibit a full embedding of this category in the category of symmetric operads with a category of objects. As an analogy to the Baez-Dolan slice construction, we exhibit a certain multicategory of function replacement as a slice construction in the multitopic setting, and use it to construct multitopes. We give an explicit description of the relationship between opetopes and multitopes.

41 pages

References in corpus (6)

• The category of opetopes and the category of opetopic sets
• Opetopic bicategories: comparison with the classical theory
• The theory of opetopes via Kelly-Mac Lane graphs
• A relationship between trees and Kelly-Mac Lane graphs
• Weak n-categories: comparing opetopic foundations
• An alternative characterisation of universal cells in opetopic n-categories

Cited by in corpus (6)

• The category of opetopes and the category of opetopic sets
• Opetopic bicategories: comparison with the classical theory
• A relationship between trees and Kelly-Mac Lane graphs
• The theory of opetopes via Kelly-Mac Lane graphs
• Weak n-categories: comparing opetopic foundations
• An alternative characterisation of universal cells in opetopic n-categories