  Batanin and Leinster's work on globular operads has provided one of many
potential defnitions of a weak $\omega$-category. Through the language of
globular operads they construct a monad whose algebras encode weak
$\omega$-categories. The purpose of this work is to show how to construct a
similar monad which will allow us to formulate weak $\omega$-categorifications
of any equational algebraic theory. We first review the classical theory of
operads and PROs. We then present how Leinster's globular operads can be
extended to a theory of globular PROs via categorical enrichment over the
category of collections. It is then shown how a process called globularization
allows us to construct from a classical PRO P a globular PRO whose algebras are
those algebras for P which are internal to the category of strict
$\omega$-categories and strict $\omega$-functors. Leinster's notion of a
contraction structure on a globular operad is then extended to this setting of
globular PROs in order to build a monad whose algebras are weakenings of the
globularization of the classica PRO P. Among these weakenings is the initial
weakining whose algebras are by construction the fully weakened
$\omega$-categorifications of the algebraic theory encoded by P.
