Homotopy theory of Spectral categories

We construct a Quillen model structure on the category of spectral categories, where the weak equivalences are the symmetric spectra analogue of the notion of equivalence of categories.Comment: 19 page

Universal suspension via Non-commutative motives

In this article we further the study of non-commutative motives. Our main result is the construction of a simple model, given in terms of infinite matrices, for the suspension in the triangulated category of non-commutative motives. As a consequence, this simple model holds in all the classical invariants such as Hochschild homology, cyclic homology and its variants (periodic, negative, ...), algebraic K-theory, topological Hochschild homology, topological cyclic homology, ...Comment: 14 page