An $\infty$-Category of 2-Segal Spaces
Fuente:
arXiv
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| Formato: | Preprint |
| Publicado: |
2024
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| _version_ | 1866915583918866432 |
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| author | Gödicke, Jonte |
| author_facet | Gödicke, Jonte |
| contents | Algebra objects in $\infty$-categories of spans admit a description in terms of $2$-Segal objects. We introduce a notion of span between $2$-Segal objects and extend this correspondence to an equivalence of $\infty$-categories. Additionally, for every $\infty$-category with finite limits $\mathcal{C}$, we introduce a notion of a birelative $2$-Segal object in $\mathcal{C}$ and establish a similar equivalence with the $\infty$-category of bimodule objects in spans. Examples of these concepts arise from algebraic and hermitian K-theory through the corresponding Waldhausen $S_{\bullet}$-construction. Apart from their categorical relevance, these concepts can be used to construct homotopy coherent representations of Hall algebras. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2407_13357 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | An $\infty$-Category of 2-Segal Spaces Gödicke, Jonte Algebraic Topology Category Theory K-Theory and Homology Algebra objects in $\infty$-categories of spans admit a description in terms of $2$-Segal objects. We introduce a notion of span between $2$-Segal objects and extend this correspondence to an equivalence of $\infty$-categories. Additionally, for every $\infty$-category with finite limits $\mathcal{C}$, we introduce a notion of a birelative $2$-Segal object in $\mathcal{C}$ and establish a similar equivalence with the $\infty$-category of bimodule objects in spans. Examples of these concepts arise from algebraic and hermitian K-theory through the corresponding Waldhausen $S_{\bullet}$-construction. Apart from their categorical relevance, these concepts can be used to construct homotopy coherent representations of Hall algebras. |
| title | An $\infty$-Category of 2-Segal Spaces |
| topic | Algebraic Topology Category Theory K-Theory and Homology |
| url | https://arxiv.org/abs/2407.13357 |