Explore the intricacies of homological 3d mirror symmetry in this advanced mathematics lecture from the M-Seminar at Kansas State University. Delve into the equivalence between the Kapustin-Rozansky-Saulina 2-category and the yet-to-be-defined "Fukaya-Fueter" 2-category associated with dual holomorphic symplectic stacks. Discover how decategorification can be applied to recover both classical and new statements in the field. Examine the toric setting, where this process yields insights into the Braden-Licata-Proudfoot-Webster hypertoric Koszul duality and a geometric interpretation of Tate's thesis. Learn about the collaborative research efforts of Benjamin Gammage, Justin Hilburn, and Aaron Mazel-Gee in this cutting-edge exploration of structural features in 3d mirror symmetry.