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arXiv · 2409.16428

Squares K-theory and 2-Segal spaces

Maxine E. Calle·Maru Sarazola
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Abstract

We define an $S_\bullet$-construction for squares categories, and introduce a class of squares categories we call "proto-Waldhausen" which capture the properties required for the $S_\bullet$-construction to model the K-theory space. The primary question we investigate is when the $S_\bullet$-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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Maxine E. Calle, Maru Sarazola. 2024-09-24. Squares K-theory and 2-Segal spaces. https://doi.org/10.2140/akt.2026.11.261

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