Nasir Sohaol

Dominions and zigzags for partially ordered monoids

An analogue of Isbells zigzag theorem for partially ordered monoids, briefly pomonoids, will be discussed. Our proof essentially consists of reducing the ordered case to the unordered one discussed in previous talk by means of certain intermediate results. In order to arrive at the main theorem, the proof of a crucial lemma will be postponed till next seminar.

References

1. Isbell J.R.: Epimorphisms and dominions, proceedings of the conference on categorical algebra, La Jolla, California, 1965, Springer, New York.
2. Renshaw J.: On free products of semigroups and a new proof of Isbells zigzag theorem, J. Algebra 251, 1215 (2002).
3. Sohail Nasir: Absolute flatness and amalgamation in pomonoids, Semigroup Forum 82, 504515 (2011).