Squares K-theory and 2-Segal spaces
K-Theory and Homology
2026-04-15 v2 Algebraic Topology
Category Theory
Abstract
We define an -construction for squares categories, and introduce a class of squares categories we call "proto-Waldhausen" which capture the properties required for the -construction to model the K-theory space. The primary question we investigate is when the -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.
Cite
@article{arxiv.2409.16428,
title = {Squares K-theory and 2-Segal spaces},
author = {Maxine E. Calle and Maru Sarazola},
journal= {arXiv preprint arXiv:2409.16428},
year = {2026}
}
Comments
Appendix removed; examples are now concentrated in a single section to improve readability; a comparison of the various relevant double-categorical structures was added in the last page