| Article ID | Journal | Published Year | Pages | File Type |
|---|---|---|---|---|
| 8904185 | Topology and its Applications | 2018 | 40 Pages |
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.
- -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.
Related Topics
Physical Sciences and Engineering
Mathematics
Geometry and Topology
Authors
Julia E. Bergner, Angélica M. Osorno, Viktoriya Ozornova, Martina Rovelli, Claudia I. Scheimbauer,