On positive opetopes, positive opetopic cardinals and positive opetopic set

2007/08/20 by Marek Zawadowski, Zawadowski, Marek
Mathematics · #18A99 #18N30 #Advanced Topology and Set Theory #FOS: Mathematics #Geometric Topology (math.GT) #Homotopy and Cohomology in Algebraic Topology #Rings, Modules, and Algebras

paper · pdf · doi:10.48550/arxiv.0708.2658

openalex publication_date 2007/08/20 · openalex created_date 2023/04/13 · openalex updated_date 2026/07/28

Abstract

We introduce the notion of a positive opetope and positive opetopic cardinals as certain finite combinatorial structures. The positive opetopic cardinals to positive-to-one polygraphs are like simple graphs to free omega-categories over omega-graphs, c.f. [MZ]. In particular, they allow us to give an explicit combinatorial description of positive-to-one polygraphs. Using this description we show, among other things, that positive-to-one polygraphs form a presheaf category with the exponent category being the category of positive opetopes. We also show that the category of omega-categories is monadic over the category of positive-to-one polygraphs with the `free functor' being an inclusion.

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