  We extend basic properties of two dimensional integrable models within the
Algebraic Bethe Ansatz approach to 2+1 dimensions and formulate the sufficient
conditions for the commutativity of transfer matrices of different spectral
parameters, in analogy with Yang-Baxter or tetrahedron equations. The basic
ingredient of our models is the R-matrix, which describes the scattering of a
pair of particles over another pair of particles, the quark-anti-quark (meson)
scattering on another quark-anti-quark state. We show that the Kitaev model
belongs to this class of models and its R-matrix fulfills well-defined
equations for integrability.
