  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).
