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The Web Monoid and Opetopic Sets

2010/11/10 by Stanisław Szawiel, Szawiel, Stanisław, Marek Zawadowski +1
Mathematics · #18D10 #18D30 #18D50 #Category Theory (math.CT) #FOS: Mathematics #math.CT #msc:18D10 #msc:18D30 #msc:18D50

paper · pdf · doi:10.48550/arxiv.1011.2374

63 pages

arxiv created 2010/11/10 · arxiv updated 2010/11/11

Abstract

We develop a new definition of opetopic sets. There are two main technical ingredients. The first is the systematic use of fibrations, which are implicit in most of the approaches in the literature. Their explicit use leads to certain clarifications in the construction of opetopic sets and other constructions. The second is the "web monoid", which plays a role analogous to the "operad for operads" of Baez and Dolan, the "multicategory of function replacement" of Hermida, Makkai and Power. We demonstrate that the web monoid is closely related to the "Baez-Dolan slice construction" as defined by Kock, Joyal, Batanin and Mascari.

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