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This work defines 2-categories of coherent sheaves, revealing equivalences that imply symplectic duality.
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.
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Gammage et al. (2026) studied this question.
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