We ask the question of how the Rees-Suskevitch theorem should be generalised to provide representations of orbit-finite 0-simple semigroups. We believe that orbit-finite groupoids will be useful for this.
A straight set is an equivariant set which is equivariantly isomorphic to a disjiont union of sets of the form . A straight semigroup is an equivariant semigroup whose universe is a straight set. We raise the following:
Question 1: is every equivariant, orbit-finite semigroup an image of some orbit-finite, straight semigroup under an equivariant mapping?
We show some simple preliminary observations towards the above question.