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arXiv · 0708.2658

On positive opetopes, positive opetopic cardinals and positive opetopic set

Marek Zawadowski
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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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Marek Zawadowski. 2023-04-11. On positive opetopes, positive opetopic cardinals and positive opetopic set. https://arxiv.org/abs/0708.2658

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