  We present a weak form of a recognition principle for Quillen model
categories due to J.H. Smith. We use it to put a model category structure on
the category of small categories enriched over a suitable monoidal simplicial
model category. The proof uses a part of the model structure on small
simplicial categories due to J. Bergner. We give an application of the weak
form of Smith's result to left Bousfield localizations of categories of monoids
in a suitable monoidal model category.
