2-Segal objects and the Waldhausen construction

Abstract

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.

References in corpus (3)

• Decomposition spaces, incidence algebras and Möbius inversion I: basic theory
• Stable Infinity Categories
• Incidence bicomodules, Möbius inversion, and a Rota formula for infinity adjunctions

Cited by in corpus (3)

• Comparison of Waldhausen constructions
• Quasi-2-Segal sets
• Higher Segal spaces and Lax ${\mathbb{A}}_{\infty }$-algebras