Nonexistence of coreflections and coproducts in some subcategories of semigroups
Peter G. Trotter · Proceedings of the American Mathematical Society · 1980
It is shown here that there are no nontrivial free regular semigroups, free regular semigroups on a semigroup or free products of regular semigroups. Analogous results are obtained in the categories of simple, bisimple and bisimple regular semigroups.