A categorical characterization of strong Steiner ω-categories

Strong Steiner ω-categories are a class of ω-categories that admit algebraic models in the form of chain complexes, whose formalism allows for several explicit computations. The conditions defining strong Steiner ω-categories are traditionally expressed in terms of the associated chain complex, making them somewhat disconnected from the ω-categorical intuition. The purpose of this paper is to characterize this class as the class of ω-categories generated by 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 ω-categories.