Beck, \(\mathcal H\) and Leech coextensions (Q1590067)

The paper investigates coextensions of monoids. A classification of Leech coextensions completing Wells' results [\textit{C.~H.~Wells}, Semigroup Forum 16, 13-35 (1978; Zbl 0394.18007)] is given. It is proved that a Leech coextension is a Beck coextension if its corresponding functor is ``centralizing''. A technical condition under which Beck coextensions are Abelian is given. Several natural conditions implying this technical condition are presented. Consequences of the general classification for special cases (regular monoids, inverse monoids, coextension groups by monoids) are derived.