  It has long been known that every weak monoidal category A is equivalent via
monoidal functors and monoidal natural transformations to a strict monoidal
category st(A). We generalise the definition of weak monoidal category to give
a definition of weak P-category for any strongly regular (operadic) theory P,
and show that every weak P-category is equivalent via P-functors and
P-transformations to a strict P-category. This strictification functor is then
shown to have an interesting universal property.
