Generalized spectral categories, topological Hochschild homology and trace maps

Abstract

Hochschild homology and trace maps GONALO TABUADA Given a monoidal model category C and an object K in C , Hovey constructed in [22] the monoidal model category Sp .C; K/ of K -symmetric spectra over C . In this paper 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 H Z-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 .