The category of hyper S-acts

Abstract

The actions of a semigroup or a monoid S on sets have been studied and applied in many branches of mathematics. In this paper, we generalize this notion, and introduce the category of hyper S-acts with the homomorphisms between them.  Then, using the usual notion of congruences defined for hyper S-acts, quotients are defined and isomorphism theorems are proved.  Finally, limits and colimits in the category of hyper S-acts are studied.