  In this paper, the Drinfeld center of a monoidal category is generalized to a
class of mixed Drinfeld centers. This gives a unified picture for the Drinfeld
center and a natural Heisenberg analogue. Further, there is an action of the
former on the latter. This picture is translated to a description in terms of
Yetter-Drinfeld and Hopf modules over quasi-bialgebras in a braided monoidal
category. Via braided reconstruction theory, intrinsic definitions of braided
Drinfeld and Heisenberg doubles are obtained, together with a generalization of
the result in [Lu94] that the Heisenberg double is a 2-cocycle twist of the
Drinfeld double for general braided Hopf algebras.
