An enrichment of KK-theory over the category of symmetric spectra

In [6] Higson showed that the formal properties of the Kasparov KK-theory groups are best understood if one regards KK(A,B) for separable C*-algebras A,B as the morphism set of a category KK. In category language the composition and exterior KKproduct give KK the structure of a symmetric monoidal ca...

Verfasser: Joachim, Michael
Stolz, Stephan
FB/Einrichtung:FB 10: Mathematik und Informatik
Dokumenttypen:Artikel
Medientypen:Text
Erscheinungsdatum:2009
Publikation in MIAMI:20.08.2009
Datum der letzten Änderung:07.04.2022
Quelle:Münster Journal of Mathematics, 2 (2009), S. 143-182
Angaben zur Ausgabe:[Electronic ed.]
Fachgebiet (DDC):510: Mathematik
Lizenz:InC 1.0
Sprache:English
Format:PDF-Dokument
URN:urn:nbn:de:hbz:6-10569461378
Permalink:https://nbn-resolving.de/urn:nbn:de:hbz:6-10569461378
Onlinezugriff:mjm_vol_2_07.pdf

In [6] Higson showed that the formal properties of the Kasparov KK-theory groups are best understood if one regards KK(A,B) for separable C*-algebras A,B as the morphism set of a category KK. In category language the composition and exterior KKproduct give KK the structure of a symmetric monoidal category which is enriched over abelian groups. We show that the enrichment of KK can be lifted to an enrichment over the category of symmetric spectra.