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<sub>l</sub> from the pointed derivator associated with the Morita homotopy theory of dg categories to a triangulated strong derivator M<sup>loc</sup> such that U<sub>l</sub> 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.

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