Rigidity of the Category of Local Modules in Braided Monoidal Categories

Explore a mathematical lecture that delves into the rigidity of local module categories within braided monoidal categories. Learn about the category of local modules C_A^{loc} as a subcategory of A-bimodules, and discover how it inherits braided monoidal structure from its parent category. Examine crucial criteria for determining when C_A^{loc} achieves rigid monoidal properties, with particular focus on applications in braided finite tensor categories. Investigate the conditions under which C_A^{loc} becomes a modular tensor category, especially when working with non-degenerate categories and symmetric Frobenius algebras. Gain insights into the Witt equivalence of non-degenerate braided finite tensor categories and related theoretical questions, supported by recent research collaborations with Harshit Yadav, Thomas Creutzig, and Robert McRae.