Homotopy coherent companionships and conjunctions

Jaco Ruit

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arXiv · 2408.14335

Homotopy coherent companionships and conjunctions

Jaco Ruit

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Abstract

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.

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Jaco Ruit. 2024-08-26. Homotopy coherent companionships and conjunctions. https://arxiv.org/abs/2408.14335

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