FRT construction for dynamical Yang–Baxter maps

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(λ) satisfying suitable conditions, a generalization of the set-theoretical solution to the quantum Yang–Baxter equation, gives birth to an (H,X)-bialgebroid AR. The categories of L-operators for R(λ) and of dynamical representations of AR are isomorphic as tensor categories.