Categorical Ambidexterity
Fuente:
arXiv
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| Format: | Preprint |
| Published: |
2024
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| _version_ | 1866910048743063552 |
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| author | Ben-Moshe, Shay |
| author_facet | Ben-Moshe, Shay |
| contents | We prove an ambidexterity result for $\infty$-categories of $\infty$-categories admitting a collection of colimits. This unifies and extends two known phenomena: the identification of limits and colimits of presentable $\infty$-categories indexed by a space, and the $\infty$-semiadditivity of the $\infty$-category of $\infty$-categories with $π$-finite colimits proven by Harpaz. Our proof employs Stefanich's universal property for the higher category of iterated spans, which encodes ambidexterity phenomena in a coherent fashion. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2411_17281 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Categorical Ambidexterity Ben-Moshe, Shay Category Theory Algebraic Topology 18N60, 18A30, 18N65 We prove an ambidexterity result for $\infty$-categories of $\infty$-categories admitting a collection of colimits. This unifies and extends two known phenomena: the identification of limits and colimits of presentable $\infty$-categories indexed by a space, and the $\infty$-semiadditivity of the $\infty$-category of $\infty$-categories with $π$-finite colimits proven by Harpaz. Our proof employs Stefanich's universal property for the higher category of iterated spans, which encodes ambidexterity phenomena in a coherent fashion. |
| title | Categorical Ambidexterity |
| topic | Category Theory Algebraic Topology 18N60, 18A30, 18N65 |
| url | https://arxiv.org/abs/2411.17281 |