Vol. 6, No. 1, 2021

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Comparison of Waldhausen constructions

Julia E. Bergner, Angélica M. Osorno, Viktoriya Ozornova, Martina Rovelli and Claudia I. Scheimbauer

Vol. 6 (2021), No. 1, 97–136
Abstract

In previous work, we developed a generalized Waldhausen S-construction whose input is an augmented stable double Segal space and whose output is a 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.

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Keywords
2-Segal spaces, Waldhausen $\sdot$-construction, double Segal spaces, model categories
Mathematical Subject Classification 2010
Primary: 18D05, 19D10, 55U40
Secondary: 18G30, 18G55, 55U10, 55U35
Milestones
Received: 10 February 2020
Accepted: 7 September 2020
Published: 8 July 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