The $S_\bullet$-construction as an equivalence between 2-Segal spaces and stable augmented double Segal spaces
Algebraic Topology
2024-12-24 v1 Category Theory
K-Theory and Homology
Abstract
This note is a contribution for a proceedings volume of the workshop "Higher Segal Spaces and their Applications to Algebraic K-Theory, Hall Algebras, and Combinatorics". The content is a streamlined exposition based on a talk about a result by Bergner-Osorno-Ozornova-Rovelli-Scheimbauer from WITII. We discuss how a generalized version of Waldhausen's S-construction describes a correspondence between 2-Segal spaces and certain double Segal spaces, which satisfy further conditions of stability and augmentation.
Cite
@article{arxiv.2412.17400,
title = {The $S_\bullet$-construction as an equivalence between 2-Segal spaces and stable augmented double Segal spaces},
author = {Martina Rovelli},
journal= {arXiv preprint arXiv:2412.17400},
year = {2024}
}