2-Segal sets and the Waldhausen construction

$2$-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.