Abstract
and the structure, of certain subsemigroups, of an inverse monoid. In this work, an analogous result is established between the Green's relation J and the D-categories of those subsemigroups. They are also given equivalent conditions for the equivalence of the D-categories of two inverse monoids and likewise equivalent conditions for the isomorphism of two inverse monoids in terms of its D-categories. It is proved that for many important classes of inverse monoids the multiplicative structure is determined by the associated category. On the contrary, a sufficient condition to obtain families of counterexamples to the above is provided and three examples are explicitely exhibited.
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