### Higher K-theory via universal invariants, by Gonçalo Tabuada

Using the formalism of Grothendieck's derivators, we construct `the universal
localizing invariant of dg categories'. By this, we mean a morphism U_{l} from
the pointed derivator associated with the Morita homotopy theory of dg
categories to a triangulated strong derivator M^{loc} such that U_{l} commutes with
filtered homotopy colimits, preserves the point, sends each exact sequence of
dg categories to a triangle and is universal for these properties.
Similary, we construct `the universal additive invariant of dg categories',
i.e. the universal morphism of derivators U_{a} to a strong triangulated
derivator M^{add} which satisfies the first two properties but the third one only
for split exact sequences. We prove that Waldhausen K-theory appears as a
mapping space in the target of the universal additive invariant.

Gonçalo Tabuada <tabuada@math.jussieu.fr>