# Comparison of Waldhausen constructions

28 May 2020 Bergner Julia E. Osorno Angélica M. Ozornova Viktoriya Rovelli Martina Scheimbauer Claudia I.

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

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• ALGEBRAIC TOPOLOGY
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