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.
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Cheng, E. An ω-category with all Duals is an ω-groupoid. Appl Categor Struct 15, 439–453 (2007). https://doi.org/10.1007/s10485-007-9081-8
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DOI: https://doi.org/10.1007/s10485-007-9081-8