Simplicial structures on model categories and functors

We produce a highly structured way of associating a simplicial category to a model category which improves on work of Dwyer and Kan and answers a ques tion of Hovey. We show that model categories satisfying a certain axiom are Quillen equivalent to simplicial model categories. A simplicial model cate gory provides higher order structure such as composable mapping spaces and homotopy colimits. We also show that certain homotopy invariant functors ca n be replaced by weakly equivalent simplicial, or "continuous," functors. T his is used to show that if a simplicial model category structure exists on a model category then it is unique up to simplicial Quillen equivalence.