Abstract: We will discuss the category small functors from a combinatorial model category to simplicial sets and introduce a model structure in which the fibrant objects are the levelwise fibrant homotopy functors. This model structure is called the homotopy model structure.

Next, we will discuss the conditions under which a Quillen equivalence of model categories induces a Quillen equivalence of the homotopy model structures. If the time permits, then we will describe an alternative model structure Quillen equivalent to the homotopy model structure.

This work is joint with D. White.