  We define a bicategory in which the 0-cells are the entwinings over variable
rings. The 1-cells are triples of a bimodule and two maps of bimodules which
satisfy an additional hexagon, two pentagons and two (co)unit triangles; and
the 2-cells are the maps of bimodules satisfying two simple compatibilities.
The operation of getting the "composed coring" from a given entwining, is
promoted here to a canonical morphism of bicategories from a bicategory of
entwinings to the Street's bicategory of corings.
