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Article Dans Une Revue Journal of Pure and Applied Algebra Année : 2023

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

Dimitri Ara
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Andrea Gagna
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Martina Rovelli
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Viktoriya Ozornova
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Résumé

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.

Dates et versions

hal-04066883 , version 1 (12-04-2023)

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Dimitri Ara, Andrea Gagna, Martina Rovelli, Viktoriya Ozornova. A categorical characterization of strong Steiner $\omega$-categories. Journal of Pure and Applied Algebra, 2023, 227 (7). ⟨hal-04066883⟩
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