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Homotopy coherent companionships and conjunctions

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arxiv 2408.14335 v2 pith:6RW3ZVPL submitted 2024-08-26 math.CT math.AT

classification math.CTmath.AT
keywords doublespacescompanionshipsconjunctionsextensionsinftysegaltheory
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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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Cited by 1 Pith paper

Reviewed papers in the Pith corpus that reference this work. Sorted by Pith novelty score. Full citation record

  1. On the squares functor and the Gaitsgory-Rozenblyum conjectures

    math.CT 2025-07 conditional novelty 7.0 of 10

    The authors prove that Gr(Ch×Dv) is naturally equivalent to C⊗D, settling Gaitsgory and Rozenblyum's final conjecture, and establish a companion-based universal property of the squares functor.

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