Squares K-theory and 2-Segal spaces
Fuente:
arXiv
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| Autori principali: | , |
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| Natura: | Preprint |
| Pubblicazione: |
2024
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| _version_ | 1866915936772030464 |
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| author | Calle, Maxine E. Sarazola, Maru |
| author_facet | Calle, Maxine E. Sarazola, Maru |
| contents | We define an $S_\bullet$-construction for squares categories, and introduce a class of squares categories we call "proto-Waldhausen" which capture the properties required for the $S_\bullet$-construction to model the K-theory space. The primary question we investigate is when the $S_\bullet$-construction of a squares category produces a 2-Segal space. We show that the answer to this question is affirmative when the squares category satisfies certain "stability" conditions. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2409_16428 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Squares K-theory and 2-Segal spaces Calle, Maxine E. Sarazola, Maru K-Theory and Homology Algebraic Topology Category Theory 19D99, 18N10, 55U10, 18G90 We define an $S_\bullet$-construction for squares categories, and introduce a class of squares categories we call "proto-Waldhausen" which capture the properties required for the $S_\bullet$-construction to model the K-theory space. The primary question we investigate is when the $S_\bullet$-construction of a squares category produces a 2-Segal space. We show that the answer to this question is affirmative when the squares category satisfies certain "stability" conditions. |
| title | Squares K-theory and 2-Segal spaces |
| topic | K-Theory and Homology Algebraic Topology Category Theory 19D99, 18N10, 55U10, 18G90 |
| url | https://arxiv.org/abs/2409.16428 |