|
|||||
|
|
|
|
|
|
|
|
|
|
|
|
|
$2$–Segal objects and
the Waldhausen construction
Julia E Bergner, Angélica M Osorno, Viktoriya Ozornova, Martina Rovelli and Claudia I Scheimbauer |
|
Algebraic & Geometric Topology 21 (2021) 1267–1326
|
Abstract |
|
In a previous paper, we showed that a discrete version of the –construction gives an equivalence of categories between –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 –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
2-Segal space, Waldhausen $S_{\bullet}$–construction,
double Segal space, model category
|
Mathematical Subject Classification 2010
Primary: 18D05, 18G55, 19D10, 55U35, 55U40
Secondary: 18G30, 55U10
|
References |
Publication
Received: 25 January 2019
Revised: 3 February 2020
Accepted: 19 June 2020
Published: 11 August 2021
|
Authors |
| Julia E Bergner | |
| Department of Mathematics University of Virginia Charlottesville, VA United States |
|
| Angélica M Osorno | |
| Department of Mathematics Reed College Portland, OR United States |
|
| Viktoriya Ozornova | |
| Fakultät für Mathematik Ruhr-Universität Bochum Bochum Germany |
|
| Martina Rovelli | |
| Mathematical Sciences
Institute The Australian National University Canberra, ACT Australia |
Department of Mathematics and
Statistics University of Massachusetts Amherst, MA United States |
| Claudia I Scheimbauer | |
| Zentrum Mathematik Technische Universität München Garching bei München Germany |
|
