Some properties of the theory of n-categories

Details Some properties of the theory of n-categories Some properties of the theory of n-categories

2001-10-25

arxiv.org/abs/math/0110273v1

Mathematics

Category Theory

Scientific paper

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.

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