Comparison of Waldhausen constructions

Abstract

In previous work, we develop a generalized Waldhausen S•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•-constructions for exact categories and for stable and exact (∞, 1)-categories, as well as the relative S•-construction for exact functors.