Two Papers: $\mathcal H$-Coextensions of Monoids; and The Structure of a Band of Groups

In the first paper, the [script capital] H-coextension problem for monoids is studied in full generality. This is done by means of a factor system technique which reduces to classical group extension theory when all monoids under consideration are groups. This technique is made possible by a correspondence between the sub-[script capital] H-congruences on a monoid and the subfunctors of a certain group-valued functor [capital Greek] Gamma. This correspondence is the precise generalization to semigroups of the basic congruence-normal subgroup correspondence for group theory. The conclusion addresses the relationships between [script capital] H-coextension theory and an appropriate cohomology theory for monoids