  After a review of the concept of "monad with arities" we show that the
category of algebras for such a monad has a canonical dense generator. This is
used to extend the correspondence between finitary monads on sets and Lawvere's
algebraic theories to a general correspondence between monads and theories for
a given category with arities. As application we determine arities for the free
groupoid monad on involutive graphs and recover the symmetric simplicial nerve
characterisation of groupoids.
