Applied Categorical Structures

, Volume 15, Issue 4, pp 439–453

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



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.


Duals ω-category ω-groupoid ω-precategory 

Mathematics Subject Classifications (2000)

18A05 18D05 18D10 18D50 57R90 


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Copyright information

© Springer Science + Business Media B.V. 2007

Authors and Affiliations

  1. 1.Department of Pure MathematicsUniversity of ChicagoChicagoUSA

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