  Notions of an (H, X)-bialgebroid and of its dynamical representation are
proposed. The dynamical representations of each (H, X)-bialgebroid form a
tensor category. Every dynamical Yang-Baxter map R(lambda) satisfying suitable
conditions, a generalization of the set-theoretical solution to the quantum
Yang-Baxter equation, gives birth to an (H, X)-bialgebroid A_R. The categories
of L-operators for R(lambda) and of dynamical representations of A_R are
isomorphic as tensor categories.
