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arXiv · 2204.12962

A categorical characterization of strong Steiner $\omega$-categories

Dimitri Ara·Andrea Gagna·Viktoriya Ozornova·Martina Rovelli
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Abstract

Strong Steiner $\omega$-categories are a class of $\omega$-categories that admit algebraic models in the form of chain complexes, whose formalism allows for several explicit computations. The conditions defining strong Steiner $\omega$-categories are traditionally expressed in terms of the associated chain complex, making them somewhat disconnected from the $\omega$-categorical intuition. The purpose of this paper is to characterize this class as the class of polygraphs that satisfy a loop-freeness condition that does not make explicit use of the associated chain complex and instead relies on the categorical features of $\omega$-categories.

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Dimitri Ara, Andrea Gagna, Viktoriya Ozornova, Martina Rovelli. 2022-04-27. A categorical characterization of strong Steiner $\omega$-categories. https://arxiv.org/abs/2204.12962

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