SAMS Subject Classification Number: 4

The representation theorem for monoids states that any monoid on a set \(X\) is isomorphic to a submonoid of the monoid of endofunctions on \(X\). In the presentation, I will give a solution to the inverse problem. That is, given a submonoid of the monoid of endofunctions of a set \(X\); when is it possible to find a monoid structure \((X, \cdot, a)\), such that the representation monoid of \((X, \cdot, a)\) is the endofunction monoid that was given. As it turns out, a simple diagrammatic argument explains the solution once we view the problem in the language of monoid actions.

This presentation is based on a Honours project under supervision of Prof. Zurab Janelidze.