Abstract

In previous work, we developed a generalized Waldhausen $S_{\bullet }$-construction whose input is an augmented stable double Segal space and whose output is a $2$-Segal space. Here, we prove that this construction recovers the previously known $S_{\bullet }$-constructions for exact categories and for stable and exact $\left(\infty ,1\right)$-categories, as well as the relative $S_{\bullet }$-construction for exact functors.

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Mathematical Subject Classification 2010

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