Presented by:
Julie Bergner
Date:
Tuesday 17th July 2018 - 14:00 to 15:00
Venue:
INI Seminar Room 2
Abstract:
The notion of unital 2-Segal space was defined independently
by Dyckerhoff-Kapranov and Galvez-Carrillo-Kock-Tonks as a generalization of a
category up to homotopy. The notion of unital 2-Segal space was defined
independently by Dyckerhoff-Kapranov and Galvez-Carrillo-Kock-Tonks as a
generalization of a category up to homotopy. A key example of both sets of
authors is that the output of applying Waldhausen's S-construction to an exact
category is a unital 2-Segal space. In joint work with Osorno, Ozornova,
Rovelli, and Scheimbauer, we expand the input of this construction to augmented
stable double Segal spaces and prove that it induces an equivalence on the
level of homotopy theories. Furthermore, we prove that exact categories and
their homotopical counterparts can be recovered as special cases of augmented
stable double Segal spaces.
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