ИСТИНА

The report is devoted to a multivalued generalization of the notions of rack and quandle, this generalization largely repeats the multivalued versions of groups and Hopf algebras. Actually, multivalued groups arose from fairly natural problems in topology and were significantly developed in the field of discrete dynamics, algebraic geometry and algebra. In the report, I will talk about the constructions of multivalued quandles, topological problems in which multivalued them occur naturally, and about an associated algebraic object, an analog of the group algebra, for multivalued quandles. The report is based on the recent joint work with V. Bardakov and T. Kozlovskaya.