This conference talk on "Completed categories and dualities" by Kevin Walker was recorded as part of the Generalized Symmetries: High-Energy, Condensed Matter and Mathematics KITP conference held at the Kavli Institute for Theoretical Physics at UC Santa Barbara. Explore cutting-edge research in quantum field theory, focusing on how symmetries can be interpreted through topological defects acting on operator spaces. The 42-minute presentation contributes to a broader conference bringing together experts examining generalized symmetries and their applications in condensed matter, high energy physics, and quantum gravity. This talk is part of a collaborative effort coordinated by Maissam Barkeshli, Michele Del Zotto, Sakura Schafer-Nameki, and Shu-Heng Shao to advance understanding of recent developments and open problems in the field.