Induced Functors on Drinfeld Centers via Monoidal Adjunctions

Explore a 49-minute lecture on induced functors on Drinfeld centers via monoidal adjunctions presented by Robert Laugwitz from the University of Nottingham. Recorded on January 9, 2024, at the Institute for Pure & Applied Mathematics (IPAM) Symmetric Tensor Categories and Representation Theory Workshop at UCLA, delve into the construction of induced (op)lax monoidal functors between corresponding Drinfeld centers given a monoidal adjunction with a valid projection formula. Discover how these functors maintain compatibility with braiding and preserve commutative (co)algebra objects. Examine specific examples, including monoidal Kleisli and Eilenberg-Moore adjunctions, as well as functors induced by extensions of Hopf algebras. Gain insights into this ongoing joint research with Johannes Flake (Bonn) and Sebastian Posur (Münster), expanding your understanding of advanced topics in category theory and representation theory.