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Seminar

DAG Seminar: 2-Segal spaces and algebraic K-theory February 26, 2019 (01:30 PM PST - 02:30 PM PST)
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Location: MSRI: Simons Auditorium
Speaker(s) Julie Bergner (University of Virginia)
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The structure of a 2-Segal space encodes data like that of a category, but for which composition need not always exist or be unique, yet is still associative.  It was shown by Dyckerhoff and Kapranov, and independently by G\'alvez-Carrillo, Kock, and Tonks, that applying Waldhausen's S-construction to an exact category results in a 2-Segal space.  In joint work with Osorno, Ozornova, Rovelli, and Scheimbauer, we expand the input of this construction in such a way that the S-construction defines an equivalence of homotopy theories, as well as recovers other known generalizations.  In work in progress with Zakharevich, we show that this general input has a close relationship with the CGW categories of Campbell and Zakharevich, which are also designed to be a very general context in which algebraic K-theory constructions can be made.

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