# Multitensors as monads on categories of enriched graphs

## 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.

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