Segal K-theory factors through Waldhausen categories

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 $C$, we produce a Waldhausen category $\Gamma (C)$ whose K-theory is weakly equivalent to the Segal K-theory of $C$. As a consequence, we show that every connective spectrum may be obtained via Waldhausen K-theory.

v3: final version to appear in Proceedings of the American Mathematical Society, 15 pages

References in corpus (3)

• Algebraic $K$-theory for squares categories
• Multicategories Model All Connective Spectra
• Squares K-theory and 2-Segal spaces