#
An algebraic definition of ($\infty$,n)-categories

##
Camell Kachour

In this paper we define a sequence of monads
$T^{(\infty,n)} (n\in\mathbb{N})$ on the category $\infty-Gr$ of
$\infty$-graphs. We conjecture that algebras for $\T^{(\infty,0)}$, which are
defined in a purely algebraic setting, are models of
$\infty$-groupoids. More generally, we conjecture that
$T^{(\infty,n)}$-algebras
are models for $(\infty,n)$-categories. We prove that our
$(\infty,0)$-categories are
bigroupoids when truncated at level 2.

Keywords:
($\infty$,n)-categories, weak $\infty$-groupoids, homotopy types

2010 MSC:
18B40,18C15, 18C20, 18G55, 20L99, 55U35, 55P15

*Theory and Applications of Categories,*
Vol. 30, 2015,
No. 22, pp 751-774.

Published 2015-06-01.

http://www.tac.mta.ca/tac/volumes/30/22/30-22.pdf

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