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Multitensors as monads on categories of enriched graphs

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Mark Weber

In this paper we unify the developments of Batanin [1998], Batanin-Weber
[2011] and Cheng [2011] into a single framework in which the interplay
between multitensors on a category $V$, and monads on the category $\cal G
V$ of graphs enriched in $V$, is taken as fundamental. The material
presented here is the conceptual background for subsequent work: in
Batanin-Cisinski-Weber [2013] the Gray tensor product of 2-categories and
the Crans [1999] tensor product of Gray categories are exhibited as
existing within our framework, and in Weber [2013] the explicit
construction of the funny tensor product of categories is generalised to a
large class of Batanin operads.

Keywords:
multitensors, enriched graphs, higher categories, higher operads

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

*Theory and Applications of Categories,*
Vol. 28, 2013,
No. 26, pp 857-932.

Published 2013-09-23.

http://www.tac.mta.ca/tac/volumes/28/26/28-26.dvi

http://www.tac.mta.ca/tac/volumes/28/26/28-26.ps

http://www.tac.mta.ca/tac/volumes/28/26/28-26.pdf

ftp://ftp.tac.mta.ca/pub/tac/html/volumes/28/26/28-26.dvi

ftp://ftp.tac.mta.ca/pub/tac/html/volumes/28/26/28-26.ps

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