2023/10/09 by Benjamin Gammage, Gammage, Benjamin, Justin Hilburn +1 · 1 citation
Mathematics · #Algebraic structures and combinatorial models #Homotopy and Cohomology in Algebraic Topology #Advanced Algebra and Geometry
paper · pdf · doi:10.48550/arxiv.2310.06172
We define 2-categories of microlocal perverse (resp. coherent) sheaves of categories on the skeleton of a hypertoric variety and show that the generators of these 2-categories lift the projectives (resp. simples) in hypertoric category O. We then establish equivalences of 2-categories categorifying the Koszul duality between Gale dual hypertoric categories O. These constructions give a prototype for understanding symplectic duality via the fully extended 3d mirror symmetry conjecture.