Generalized spectral categories, topological Hochschild homology and trace maps

per we describe how to lift a model structure on the category of C–enriched categories to the category of Sp†.C;K/–enriched categories. This allow us to construct a (four step) zig-zag of Quillen equivalences comparing dg categories to HZ–categories. As an application we obtain: (1) the invariance under weak equivalences of the topological Hochschild homology (THH) and topological cyclic homology (TC) of dg categories; (2) non-trivial natural transformations from algebraic K–theory to THH