Segal K-theory factors through Waldhausen categories
Fuente:
arXiv
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| Autores principales: | , |
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| Formato: | Preprint |
| Publicado: |
2025
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| _version_ | 1866914387219972096 |
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| author | Calle, Maxine E. Chan, David |
| author_facet | Calle, Maxine E. Chan, David |
| contents | 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2506_13732 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Segal K-theory factors through Waldhausen categories Calle, Maxine E. Chan, David K-Theory and Homology Algebraic Topology 19D23 (primary), 18F25, 55P42 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. |
| title | Segal K-theory factors through Waldhausen categories |
| topic | K-Theory and Homology Algebraic Topology 19D23 (primary), 18F25, 55P42 |
| url | https://arxiv.org/abs/2506.13732 |