# nLab opetope

### Context

#### Higher category theory

higher category theory

# Contents

## Idea

Opetopes are one of the geometric shapes of cells in the approach to the higher category theory of n-categories and ω-categories put forward by John Baez and James Dolan.

## References

An overview is in chapter 4 of

and in chapter 7 of

Opetopes were introduced here:

• John Baez and James Dolan, Higher-dimensional algebra III: $n$-categories and the algebra of opetopes, Adv. Math. 135 (1998), 145–206. (arXiv)

Some mistakes were corrected in subsequent papers:

• Eugenia Cheng, The category of opetopes and the category of opetopic sets, Th. Appl. Cat. 11 (2003), 353–374. arXiv)

• Tom Leinster, Structures in higher-dimensional category theory. (arXiv)

Makkai and collaborators introduced a slight variation they called ‘multitopes’:

• Claudio Hermida, Michael Makkai, and J. Power: On weak higher-dimensional categories I, II. Jour. Pure Appl. Alg. 157 (2001), 221–277.

• Michael Makkai, The multitopic $\omega$-category of all multitopic $\omega$-categories. (online)

Cheng has carefully compared opetopes and multitopes, and various approaches to opetopic $n$-categories:

• Eugenia Cheng, Weak $n$-categories: opetopic and multitopic foundations, Jour. Pure Appl. Alg. 186 (2004), 109–137.(arXiv)

• Eugenia Cheng, Weak $n$-categories: comparing opetopic foundations, Jour. Pure Appl. Alg. 186 (2004), 219–231. (arXiv)

She has also shown that opetopic bicategories are “the same” as the ordinary kind:

A formalization of the definition of opetotes in type theory is in

• Eric Finster, Type theory and the opetopes, HDACT Ljubljana, June 2012 (pdf)

Revised on June 10, 2013 14:36:07 by Urs Schreiber (89.204.137.122)