#
Simplicial Nerve of an $A_\infty$-category

##
Giovanni Faonte

We introduce a functor called the simplicial nerve of an
$A_\infty$-category defined on the category of
$A_\infty$-categories with values in simplicial sets. We show
that the nerve of an $A_\infty$-category is an
$(\infty,1)$-category in the sense of J. Lurie. This
construction generalizes the nerve construction for differential graded
categories given by Lurie. We prove that if a differential graded
category is pretriangulated in the sense of A.I. Bondal and M. Kapranov
then its nerve is a stable $(\infty,1)$-category in the sense of
J. Lurie.

Keywords:
$A_\infty$-categories, nerve, higher categories, pretriangulated
dg-categories

2010 MSC:
18G30

*Theory and Applications of Categories,*
Vol. 32, 2017,
No. 2, pp 31-52.

Published 2017-01-16.

http://www.tac.mta.ca/tac/volumes/32/2/32-02.pdf

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