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arXiv · 1609.02853

2-Segal sets and the Waldhausen construction

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

It is known by results of Dyckerhoff-Kapranov and of G\'alvez--Carrillo-Kock-Tonks that the output of the Waldhausen S.-construction has a unital 2-Segal structure. Here, we prove that a certain S.-functor defines an equivalence between the category of augmented stable double categories and the category of unital 2-Segal sets. The inverse equivalence is described explicitly by a path construction. We illustrate the equivalence for the known examples of partial monoids, cobordism categories with genus constraints and graph coalgebras.

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BibTeXRIS

Julia E. Bergner, Angélica M. Osorno, Viktoriya Ozornova, Martina Rovelli, Claudia I. Scheimbauer. 2016-09-09. 2-Segal sets and the Waldhausen construction. https://arxiv.org/abs/1609.02853

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