FAITHFUL FUNCTORS FROM CANCELLATIVE CATEGORIES TO CANCELLATIVE MONOIDS WITH AN APPLICATION TO ABUNDANT SEMIGROUPS
Victoria A. R. Gould, Mark Kambites · International Journal of Algebra and Computation · 2005
We prove that any small cancellative category admits a faithful functor to a cancellative monoid. We use our result to show that any primitive ample semigroup is a full subsemigroup of a Rees matrix semigroup [Formula: see text] where M is a cancellative monoid and P is the identity matrix. On the other hand a consequence of a recent result of Steinberg is that it is undecidable whether a finite ample semigroup embeds as a full subsemigroup of an inverse semigroup.