Homotopy coherent companionships and conjunctions
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arXiv
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| Format: | Preprint |
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2024
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| _version_ | 1866915232829407232 |
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| author | Ruit, Jaco |
| author_facet | Ruit, Jaco |
| contents | We demonstrate that companionships and conjunctions in double $\infty$-categories -- and more generally, in double Segal spaces -- extend to functors out of the free-living companionship and conjunction respectively. Specifically, we prove that these extensions are (homotopically) unique: the corresponding spaces of extensions are contractible under suitable completeness assumptions. The developed theory is then put to use to give a characterization of companions and conjoints in functor double Segal spaces in terms of so-called companionable and conjointable 2-cells. We end with an application of our results to $(\infty,2)$-category theory. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2408_14335 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Homotopy coherent companionships and conjunctions Ruit, Jaco Category Theory Algebraic Topology 18N65, 55U35, 18N10 We demonstrate that companionships and conjunctions in double $\infty$-categories -- and more generally, in double Segal spaces -- extend to functors out of the free-living companionship and conjunction respectively. Specifically, we prove that these extensions are (homotopically) unique: the corresponding spaces of extensions are contractible under suitable completeness assumptions. The developed theory is then put to use to give a characterization of companions and conjoints in functor double Segal spaces in terms of so-called companionable and conjointable 2-cells. We end with an application of our results to $(\infty,2)$-category theory. |
| title | Homotopy coherent companionships and conjunctions |
| topic | Category Theory Algebraic Topology 18N65, 55U35, 18N10 |
| url | https://arxiv.org/abs/2408.14335 |