English

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).

Keywords

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

R2 v1 2026-06-24T08:23:56.051Z