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Monoid extensions and the Grothendieck construction

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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).

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Correspondence to Graham Manuell.

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Communicated by Mark V. Lawson.

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The author acknowledges financial support from the Centre for Mathematics of the University of Coimbra (UIDB/00324/2020, funded by the Portuguese Government through FCT/MCTES).

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Manuell, G. Monoid extensions and the Grothendieck construction. Semigroup Forum 105, 488–507 (2022). https://doi.org/10.1007/s00233-022-10294-2

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  • DOI: https://doi.org/10.1007/s00233-022-10294-2

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