Comparison of Waldhausen constructions

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

doi:10.2140/akt.2021.6.97

Comparison of Waldhausen constructions

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

Assistant Professorship of Topology

Research output: Contribution to journal › Article › peer-review

Abstract

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

Original language	English
Pages (from-to)	97-136
Number of pages	40
Journal	Annals of K-Theory
Volume	6
Issue number	1
DOIs	https://doi.org/10.2140/akt.2021.6.97
State	Published - 2021

Keywords

2-Segal spaces
Double Segal spaces
Model categories
Waldhausen S∙-construction

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10.2140/akt.2021.6.97

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AU - Bergner, Julia E.

AU - Osorno, Angélica M.

AU - Ozornova, Viktoriya

AU - Rovelli, Martina

AU - Scheimbauer, Claudia I.

PY - 2021

Y1 - 2021

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

KW - 2-Segal spaces

KW - Double Segal spaces

KW - Model categories

KW - Waldhausen S∙-construction

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JO - Annals of K-Theory

JF - Annals of K-Theory

IS - 1

ER -

Comparison of Waldhausen constructions

Abstract

Keywords

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