Quantum annular homology and bigger Burnside categories (Q6591057)

\textit{T. Lawson} et al. [Geom. Topol. 24, No. 2, 623--745 (2020; Zbl 1515.57015)] used the Burnside \(2\)-category of the trivial group for the construction of a finite suspension spectrum realizing Khovanov homology by associating a functor \(F(D)\) from the cube category to the Burnside category, where \(D\) is a link diagram.\N\NIn this paper the authors extend this realization functor to several enlargements of the Burnside category, namely the locally finite Burnside category, the bilocally finite Burnside category, and the Burnside category with an action of a group \(G\). They use this construction to associate a locally compact spectrum to a link diagram in the annulus, which is independent of the diagram and recovers the quantum annular Khovanov homology of \textit{A. Beliakova} et al. [Invent. Math. 215, No. 2, 383--492 (2019; Zbl 1411.57021)].