Monoid extensions and the Grothendieck construction
Category Theory
2023-06-28 v2 Rings and Algebras
Abstract
In category theory circles it is well-known that the Schreier theory of group extensions can be understood in terms of the Grothendieck construction on indexed categories. However, it is seldom discussed how this relates to extensions of monoids. We provide an introduction to the generalised Grothendieck construction and apply it to recover classifications of certain classes of monoid extensions (including Schreier and weakly Schreier extensions in particular).
Cite
@article{arxiv.2112.10288,
title = {Monoid extensions and the Grothendieck construction},
author = {Graham Manuell},
journal= {arXiv preprint arXiv:2112.10288},
year = {2023}
}
Comments
17 pages. Added an example and clarified a remark. To appear in Semigroup Forum