Segal K-theory factors through Waldhausen categories
K-Theory and Homology
2026-03-13 v3 Algebraic Topology
Abstract
We show that Segal's K-theory of symmetric monoidal categorizes can be factored through Waldhausen categories. In particular, given a symmetric monoidal category , we produce a Waldhausen category whose K-theory is weakly equivalent to the Segal K-theory of . As a consequence, we show that every connective spectrum may be obtained via Waldhausen K-theory.
Keywords
Cite
@article{arxiv.2506.13732,
title = {Segal K-theory factors through Waldhausen categories},
author = {Maxine E. Calle and David Chan},
journal= {arXiv preprint arXiv:2506.13732},
year = {2026}
}
Comments
v3: final version to appear in Proceedings of the American Mathematical Society, 15 pages