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arXiv · 1809.10924

2-Segal objects and the Waldhausen construction

Julia E. Bergner·Angélica M. Osorno·Viktoriya Ozornova·Martina Rovelli·Claudia I. Scheimbauer
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Abstract

In a previous paper, we showed that a discrete version of the $S_\bullet$-construction gives an equivalence of categories between unital 2-Segal sets and augmented stable double categories. Here, we generalize this result to the homotopical setting, by showing that there is a Quillen equivalence between a model category for unital 2-Segal objects and a model category for augmented stable double Segal objects which is given by an $S_\bullet$-construction. We show that this equivalence fits together with the result in the discrete case and briefly discuss how it encompasses other known $S_\bullet$-constructions.

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Julia E. Bergner, Angélica M. Osorno, Viktoriya Ozornova, Martina Rovelli, Claudia I. Scheimbauer. 2018-09-28. 2-Segal objects and the Waldhausen construction. https://doi.org/10.2140/agt.2021.21.1267

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