Geodesic
A simple criterion for extending natural transformations to higher $K$-theory
Documenta mathematica, Tome 16 (2011), pp. 657-668
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In this article we introduce a very simple an widely applicable criterion for extending natural transformations to higher K-theory. More precisely, we prove that every natural transformation defined on the Grothendieck group and with values in an additive theory admits a unique extension to higher K-theory. As an application, the higher trace maps and the higher Chern characters originally constructed by Dennis and Karoubi, respectively, can be obtained in an elegant, unified, and conceptual way from our general results.
DOI : 10.4171/dm/346
Classification : 19D55
Mots-clés : higher K-theory, higher trace maps, higher Chern characters, non-commutative motives 
@article{10_4171_dm_346,
     author = {Gon\c{c}alo Tabuada},
     title = {A simple criterion for extending natural transformations to higher $K$-theory},
     journal = {Documenta mathematica},
     pages = {657--668},
     year = {2011},
     volume = {16},
     doi = {10.4171/dm/346},
     url = {http://geodesic.mathdoc.fr/articles/10.4171/dm/346/}
}
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Gonçalo Tabuada. A simple criterion for extending natural transformations to higher $K$-theory. Documenta mathematica, Tome 16 (2011), pp. 657-668. doi: 10.4171/dm/346

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