Multisemigroups

Multisemigroups are "semigroups in which the semigroup operation is mulivalued". Multisemigroups appear naturally in higher representation theory as they describe combinatorics of additive 2-categories. In this talk I will try to explain how multisemigroups appear, give many examples of multisemigroups and discuss similarities and differences between multisemigroups and semigroups.