Quotients of monoid extensions and their interplay with Baer sums

Cosetal extensions of monoids generalise extensions of groups, special Schreier extensions of monoids and Leech's normal extensions of groups by monoids. They share a number of properties with group extensions, including a notion of Baer sum when the kernel is abelian. However, unlike group ext...

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Bibliographic Details
Published in:arXiv.org 2022-01
Main Authors: Faul, Peter, Manuell, Graham
Format: Article
Language:English
Subjects:
Homology
Monoids
Quotients
Online Access:Get full text
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Summary:Cosetal extensions of monoids generalise extensions of groups, special Schreier extensions of monoids and Leech's normal extensions of groups by monoids. They share a number of properties with group extensions, including a notion of Baer sum when the kernel is abelian. However, unlike group extensions (with fixed kernel and cokernel) there may be nontrivial morphisms between them. We explore the structure of the category of cosetal extensions and relate it to an analogue of second cohomology groups. Finally, the order structure and additive structures are combined to give an indexed family of inverse semigroups of extensions. These in turn can be combined into an inverse category.
ISSN:2331-8422
DOI:10.48550/arxiv.2006.10537