Localization for $THH(ku)$ and the Topological Hochschild and Cyclic Homology of Waldhausen Categories

The authors develop a theory of $THH$ and $TC$ of Waldhausen categories and prove the analogues of Waldhausen's theorems for $K$-theory. They resolve the longstanding confusion about localization sequences in $THH$ and $TC$, and establish a specialized devissage theorem.