2024/08/26 by Jaco Ruit, Ruit, Jaco · 1 citation
Mathematics · Medicine · #Homotopy and Cohomology in Algebraic Topology #Algebraic structures and combinatorial models #Intracranial Aneurysms: Treatment and Complications
paper · pdf · doi:10.48550/arxiv.2408.14335
We demonstrate that companionships and conjunctions in double ∞-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 (∞,2)-category theory.