Multitensors as Monads on Categories of Enriched Graphs
نویسنده
چکیده
In this paper we unify the developments of [Batanin, 1998], [BataninWeber, 2011] and [Cheng, 2011] into a single framework in which the interplay between multitensors on a category V , and monads on the category GV 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 2categories and the Crans tensor product [Crans, 1999] 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.
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