Deconstructing span categories for profinite groups
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arXiv
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| Format: | Preprint |
| Published: |
2026
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| _version_ | 1866908765281845248 |
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| author | Barnes, David Taggart, Niall |
| author_facet | Barnes, David Taggart, Niall |
| contents | One of the major advantages of $\infty$-category theory over classical $1$-category theory is its robust and homotopically meaningful framework for taking (co)limits of diagrams of $\infty$-categories. However, it is both subtle and crucial to specify which variant of the $\infty$-category of $\infty$-categories is being used when forming such (co)limits. In this article, we present a concrete case study illustrating how (co)limits of $\infty$-categories behave in a specific setting. We demonstrate that the span category of a profinite group can be realised as the colimit of the span categories of its quotients by open normal subgroups and provide a number of applications to the world of equivariant (higher) algebra. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2601_09544 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Deconstructing span categories for profinite groups Barnes, David Taggart, Niall Category Theory Algebraic Topology 18N60, 55P91 One of the major advantages of $\infty$-category theory over classical $1$-category theory is its robust and homotopically meaningful framework for taking (co)limits of diagrams of $\infty$-categories. However, it is both subtle and crucial to specify which variant of the $\infty$-category of $\infty$-categories is being used when forming such (co)limits. In this article, we present a concrete case study illustrating how (co)limits of $\infty$-categories behave in a specific setting. We demonstrate that the span category of a profinite group can be realised as the colimit of the span categories of its quotients by open normal subgroups and provide a number of applications to the world of equivariant (higher) algebra. |
| title | Deconstructing span categories for profinite groups |
| topic | Category Theory Algebraic Topology 18N60, 55P91 |
| url | https://arxiv.org/abs/2601.09544 |