2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/174836We 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.12 pagesRings and AlgebrasCategory Theory16W30; 18C15; 18D05text