Segal K-theory factors through Waldhausen categories

2025/06/16 by Maxine E. Calle, David Chan, Calle, Maxine E. +1
Mathematics · #18F25 #19D23 (primary) #55P42 #Advanced Topics in Algebra #Algebraic Topology (math.AT) #Algebraic structures and combinatorial models #FOS: Mathematics #Homotopy and Cohomology in Algebraic Topology #K-Theory and Homology (math.KT)

paper · pdf · doi:10.48550/arxiv.2506.13732

openalex publication_date 2025/06/16 · openalex created_date 2025/10/13 · openalex updated_date 2026/07/28

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 Γ(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.

Citations

• Squares K-theory and 2-Segal spaces
• Equivariant algebraic K-theory of symmetric monoidal Mackey functors
• Algebraic K-theory for squares categories
• 2-Dimensional Categories
• Stable homotopy hypothesis in the Tamsamani model
• The equivariant parametrized h-cobordism theorem, the non-manifold part

Related

• Waldhausen's S_\bullet-construction
• A remark on K-theory and S-categories
• Higher Segal structures in algebraic K-theory
• Squares K-theory and 2-Segal spaces
• Lax Diagrams and Enrichment