FROM RELATION TO EMULATION - THE COVERING LEMMA FOR TRANSFORMATION SEMIGROUPS

We define the kernel of a relational morphism of finite or infinite, f aithful or non-faithful transformation semigroups. We prove the coveri ng lemma for transformation semigroups, and a wreath product embedding theorem in terms of this kernel. Applications easily obtained using t his new language include a global embedding theorem for light simple s emigroups without idempotents, a proof of the Krohn-Rhodes theorem, an d some results about transformation groups.