Topological Hochschild and cyclic homology for Differential graded   categories
  We define a topological Hochschild (THH) and cyclic (TC) homology theory for differential graded (dg) categories and construct several non-trivial natural transformations from algebraic K-theory to THH(-).   In an intermediate step, we prove that the homotopy theory of dg categories is Quillen equivalent, through a four step zig-zag of Quillen equivalences, to the homotopy theory of Eilenberg-Mac Lane spectral categories.   Finally, we show that over the rationals two dg categories are topological equivalent if and only if they are quasi-equivalent. 
Goncalo Tabuada