  We relate the old and new cohomology monoids of an arbitrary monoid $M$ with
coefficients in semimodules over $M$, introduced in the author's previous
papers, to monoid and group extensions. More precisely, the old and new second
cohomology monoids describe Schreier extensions of semimodules by monoids, and
the new third cohomology monoid is related to a certain group extension
problem.
