  Knop constructed a tensor category associated to a finitely-powered regular
category equipped with a degree function. In recent work with Harman, we
constructed a tensor category associated to an oligomorphic group equipped with
a measure. In this paper, we explain how Knop's approach fits into our theory.
The first, and most important, step describes finitely-powered regular
categories in terms of oligomorphic monoids; this may be of independent
interest. We go on to examine some aspects of this construction when the
regular category one starts with is the category of $G$-sets for an
oligomorphic group $G$, which yields some interesting examples.
