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2-Segal objects and the Waldhausen construction. (arXiv:1809.10924v1 [math.AT])
来源于:arXiv
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. 查看全文>>