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Multitensor lifting and strictly unital higher category theory

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Michael Batanin, Denis-Charles Cisinski and Mark Weber

In this article we extend the theory of lax monoidal structures, also
known as multitensors, and the monads on categories of enriched graphs
that they give rise to. Our first principal result - the lifting theorem
for multitensors - enables us to see the Gray tensor product of
2-categories and the Crans tensor product of Gray categories as part of
this framework. We define weak $n$-categories with strict units by means
of a notion of reduced higher operad, using the theory of algebraic weak
factorisation systems. Our second principal result is to establish a lax
tensor product on the category of weak $n$-categories with strict units,
so that enriched categories with respect to this tensor product are
exactly weak (n+1)-categories with strict units.

Keywords:
multitensors, strictly unital higher categories, higher operads

2010 MSC:
18A05; 18D20; 18D50; 55P48

*Theory and Applications of Categories,*
Vol. 28, 2013,
No. 25, pp 804-856.

Published 2013-09-23.

http://www.tac.mta.ca/tac/volumes/28/25/28-25.dvi

http://www.tac.mta.ca/tac/volumes/28/25/28-25.ps

http://www.tac.mta.ca/tac/volumes/28/25/28-25.pdf

ftp://ftp.tac.mta.ca/pub/tac/html/volumes/28/25/28-25.dvi

ftp://ftp.tac.mta.ca/pub/tac/html/volumes/28/25/28-25.ps

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