Given a monoidal adjunction for which the projection formula holds, we construct induced (op)lax monoidal functors between the corresponding Drinfeld centers. These functors are compatible with braiding and hence preserve commutative (co)algebra objects. As classes of examples, we consider monoidal Kleisli and Eilenberg-Moore adjunctions as well as functors induced by extensions of Hopf algebras. This is joint work in progress with Johannes Flake (Bonn) and Sebastian Posur (Münster).
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