English

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 CC, we produce a Waldhausen category Γ(C)\Gamma(C) whose K-theory is weakly equivalent to the Segal K-theory of CC. 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