Monoid Extensions, Relaxed Actions and Cohomology

In this thesis a particular class of monoid extensions are studied and characterized, the weakly Schreier split extensions. It is demonstrated that both Artin glueings of frames and λ-semidirect products of inverse semigroups are examples of these extensions. The characterization is given in terms of a generalization of an action. This makes the theory amenable to cohomological ideas. Specifically, a new class of extensions called cosetal extensions are introduced and characterized. When parameterized by this new notion of action, a Baer sim may be defined in these extensions giving rise to an analogue of the second cohomology group. Finally, a connection is made to the setting of toposes, exploiting the link between toposes and frames.

Name dc:type.qualificationname

Doctor of Philosophy (PhD)

Level dc:type.qualificationlevel

Doctoral

Grantor dc:publisher.institution

University of Cambridge

Year dc:date.issued

2020

Author dc:creator

• Faul, Peter

Advisor dc:contributor.advisor

• Johnstone, Peter

• Monoid
• Extension
• Schreier
• Topos
• Frame
• Artin glueing

Licence

• https://apollo8-f-pro.lib.cam.ac.uk/bitstreams/91e07072-303c-447d-bf30-48f644299ac8/download
• https://creativecommons.org/licenses/by/4.0/

Language dc:language

eng

DOI dc:identifier.doi

https://doi.org/10.17863/CAM.69869

OAI identifier oai:identifier

oai:www.repository.cam.ac.uk:1810/322412