Abstract Martina Rovelli

Title: 2-Segal sets and the Waldhausen construction 

Abstract: 2-Segal objects, which are a generalisation of ordinary Segal objects, were introduced and studied by Dyckerhoff-Kapranov and Gálvez-Kock-Tonks. An important example of a 2-Segal object is the Waldhausen construction of an exact category. The Waldhausen construction makes sense for a more general input, and the goal of the talk is to explain that, in the discrete setting, the Waldhausen construction is in fact quite exhaustive. More precisely, it induces an equivalence between the category of stable pointed double categories and the category of reduced unital 2-Segal sets. This is joint work with Bergner, Osorno, Ozornova and Scheimbauer.

 References for 2-Segal spaces and decomposition spaces:

The work of Dyckerhoff and Kapranov: Higher Segal spaces I, https://arxiv.org/pdf/1212.3563.pdf

The series of papers by Gálvez-Carrillo, Kock and Tonks: Decomposition Spaces, Incidence Algebras and Möbius Inversion, https://arxiv.org/pdf/1404.3202.pdf.

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