Geodesic
Multitensors as monads on categories of enriched graphs
Theory and applications of categories, Tome 28 (2013), pp. 857-932

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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.

Publié le :
Classification : 18A05, 18D20, 18D50, 55P48
Keywords: multitensors, enriched graphs, higher categories, higher operads 
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     author = {Mark Weber},
     title = {Multitensors as monads on categories of enriched graphs},
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     pages = {857--932},
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     volume = {28},
     year = {2013},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/TAC_2013_28_a25/}
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Mark Weber. Multitensors as monads on categories of enriched graphs. Theory and applications of categories, Tome 28 (2013), pp. 857-932. http://geodesic.mathdoc.fr/item/TAC_2013_28_a25/