2-Segal objects and the Waldhausen construction
Algebraic Topology
2021-08-18 v1 Category Theory
K-Theory and Homology
Abstract
In a previous paper, we showed that a discrete version of the -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 -construction. We show that this equivalence fits together with the result in the discrete case and briefly discuss how it encompasses other known -constructions.
Keywords
Cite
@article{arxiv.1809.10924,
title = {2-Segal objects and the Waldhausen construction},
author = {Julia E. Bergner and Angélica M. Osorno and Viktoriya Ozornova and Martina Rovelli and Claudia I. Scheimbauer},
journal= {arXiv preprint arXiv:1809.10924},
year = {2021}
}