  2-Theories are a canonical way of describing categories with extra structure.
2-theory-morphisms are used when discussing how one structure can be replaced
with another structure. This is central to categorical coherence theory. We
place a Quillen model category structure on the category of 2-theories and
2-theory-morphisms where the weak equivalences are biequivalences of
2-theories. A biequivalence of 2-theories (Morita equivalence) induces and is
induced by a biequivalence of 2-categories of algebras. This model category
structure allows one to talk of the homotopy of 2-theories and discuss the
universal properties of coherence.
