Semigroup expansions using the derived category, kernel, and Malcev products Original Research Article

Three new classes of expansions are defined in this paper. More precisely, three different expansions are associated to each semigroup variety V. It is shown that several previously defined expansions can be viewed as specific examples of these constructions, or slight variants there of. This method is then used to “smooth” an already existing expansion to one which is guaranteed to be functorial and is maximal in a sense that will be made precise. Perhaps more importantly, this method of construction provides a large resource of expansions to be used as needed in the future.