Higher K-theory via universal invariants
| dc.creator | Tabuada, Goncalo | |
| dc.date | 2007-06-16 | |
| dc.date | 2008-09-18 | |
| dc.date.accessioned | 2026-07-07T10:03:21Z | |
| dc.date.available | 2026-07-07T10:03:21Z | |
| dc.description | 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 `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. This is the first conceptual characterization of Quillen-Waldhausen's K-theory since its definition in the early 70's. As an application we obtain for free the higher Chern characters from K-theory to cyclic homology. | |
| dc.description | 61 pages. Section 17 is new. Cosmetic changes | |
| dc.identifier | https://arxiv.org/abs/0706.2420 | |
| dc.identifier | http://arxiv.org/abs/0706.2420 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/169259 | |
| dc.subject | K-Theory and Homology | |
| dc.subject | Algebraic Topology | |
| dc.subject | 18G55, 18F20, 18E30 (Primary) 19D35, 19D55 (Secondary) | |
| dc.title | Higher K-theory via universal invariants | |
| dc.type | text |