# Some properties of the theory of n-categories

Abstract : Let $L_n$ denote the Dwyer-Kan localization of the category of weak n-categories divided by the n-equivalences. We propose a list of properties that this simplicial category is likely to have, and conjecture that these properties characterize $L_n$ up to equivalence. We show, using these properties, how to obtain the morphism $n-1$-categories between two points in an object of $L_n$ and how to obtain the composition map between the morphism objects.
Document type :
Preprints, Working Papers, ...

https://hal.archives-ouvertes.fr/hal-00118005
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Submitted on : Sunday, December 3, 2006 - 10:56:33 PM
Last modification on : Friday, January 12, 2018 - 1:52:00 AM

### Citation

Carlos Simpson. Some properties of the theory of n-categories. 2001. ⟨hal-00118005⟩

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