The Injective Envelope of S-Sets

Abstract

If S is a semigroup, then an S-set AS is a set A together with a representation of S by mappings of A into itself. In this article, the theory of injective envelopes is carried from R-modules to S-sets. These results are known to hold in every Grothendieck category, but the category EnsS of (right) S-sets is not even additive.