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2-Segal sets and the Waldhausen construction

Abstract:
It is known by results of Dyckerhoff–Kapranov and of Gálvez-Carrillo–Kock–Tonks that the output of the Waldhausen S • -construction has a unital 2-Segal structure. Here, we prove that a certain S • -functor defines an equivalence between the category of augmented stable double categories and the category of unital 2-Segal sets. The inverse equivalence is described explicitly by a path construction. We illustrate the equivalence for the known examples of partial monoids, cobordism categories with genus constraints and graph coalgebras.
Publication status:
Published
Peer review status:
Peer reviewed
Version:
Accepted manuscript

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Publisher copy:
10.1016/j.topol.2017.12.009

Authors


Bergner, JE More by this author
Osorno, AM More by this author
Ozornova, V More by this author
Rovelli, M More by this author
More by this author
Institution:
University of Oxford
Division:
MPLS Division
Department:
Mathematical Institute
National Science Foundation More from this funder
Simons Foundation More from this funder
Swiss National Science Foundation More from this funder
Publisher:
Elsevier Publisher's website
Journal:
Topology and its Applications Journal website
Volume:
235
Pages:
445-484
Publication date:
2017-12-06
Acceptance date:
2017-04-25
DOI:
EISSN:
1879-3207
ISSN:
0166-8641
Pubs id:
pubs:853874
URN:
uri:d48f7e7c-4f7d-4f65-8b7e-96b2df82999d
UUID:
uuid:d48f7e7c-4f7d-4f65-8b7e-96b2df82999d
Local pid:
pubs:853874

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