Abstract
We characterize those semigroups with local units which are Morita equivalent to semigroups with local units having commuting idempotents. A key element in this characterization is a description of those inverse categories which are equivalent to Cauchy completions of inverse semigroups.
2000 Mathematics Subject Classification:
ACKNOWLEDGMENTS
The first author would like to thank Aleppo University, Syria, and the British Council for their support. The second author would like to thank Lauri Tart for an e-mail that led him to simplify the definition of local isomorphism. Both authors would like to thank Professors Valdis Laan and Laci Márki for generously sharing their ideas on the Morita theory of semigroups, and the anonymous referee for his or her detailed comments and suggestions.
Notes
Communicated by V. Gould.