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The $S_\bullet$-construction as an equivalence between 2-Segal spaces and stable augmented double Segal spaces (2412.17400v1)
Published 23 Dec 2024 in math.AT, math.CT, and math.KT
Abstract: This note is a contribution for a proceedings volume of the workshop "Higher Segal Spaces and their Applications to Algebraic K-Theory, Hall Algebras, and Combinatorics". The content is a streamlined exposition based on a talk about a result by Bergner-Osorno-Ozornova-Rovelli-Scheimbauer from WITII. We discuss how a generalized version of Waldhausen's S-construction describes a correspondence between 2-Segal spaces and certain double Segal spaces, which satisfy further conditions of stability and augmentation.
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