Squares K-theory and 2-Segal spaces
Abstract
We define an S-construction for squares categories, and introduce a class of squares categories we call "proto-Waldhausen" which capture the properties required for the S-construction to model the K-theory space. The primary question we investigate is when the S-construction of a squares category produces a 2-Segal space. We show that the answer to this question is affirmative when the squares category satisfies certain "stability" conditions.
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