An algebraic theory of hypergroups

The category of groups forms a full subcategory of the category of hypergroups. This larger category also contains other group theoretic objects, such as the conjugacy class hypergroup and character hypergroup of a finite group. Definitions of hypergroups and hypergroup morphisms are given and related to double algebras (which are simultaneously algebras and cogebras, but not Hopf algebras in general). Quotient and orbit hypergroups are defined. Coefficients are allowed in a more or less arbitrary field. These concepts provide a new language in which groups and their character tables can be fruitfully discussed.