Applied Categorical Structures

, Volume 15, Issue 4, pp 439–453

An ω-category with all Duals is an ω-groupoid

Article

DOI: 10.1007/s10485-007-9081-8

Cite this article as:
Cheng, E. Appl Categor Struct (2007) 15: 439. doi:10.1007/s10485-007-9081-8

Abstract

We make a definition of ω-precategory which should underlie any definition of weak ω-category. We make a precise definition of pseudo-invertible cells in this setting. We show that in an ω-precategory with all weak duals, every cell is pseudo-invertible. We deduce that in any “sensible” theory of ω-categories, an ω-category with all weak duals is an ω-groupoid. We discuss various examples and open questions involving higher-dimensional tangles and cobordisms.

Keywords

Duals ω-category ω-groupoid ω-precategory 

Mathematics Subject Classifications (2000)

18A05 18D05 18D10 18D50 57R90 

Copyright information

© Springer Science + Business Media B.V. 2007

Authors and Affiliations

  1. 1.Department of Pure MathematicsUniversity of ChicagoChicagoUSA