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Transactions of the American Mathematical Society

ISSN 1088-6850(online) ISSN 0002-9947(print)

 

 

KV-theory of categories


Author: Charles A. Weibel
Journal: Trans. Amer. Math. Soc. 267 (1981), 621-635
MSC: Primary 18F25
DOI: https://doi.org/10.1090/S0002-9947-1981-0626494-7
MathSciNet review: 626494
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Abstract: Quillen has constructed a $ K$-theory $ {K_{\ast}}C$ for nice categories, one of which is the category of projective $ R$-modules. We construct a theory $ K{V_{\ast}}C$ for the nice categories parametrized by rings. When applied to projective modules we recover the Karoubi-Villamayor $ K$-theory $ K{V_{\ast}}(R)$.

As an application, we show that the Cartan map from $ {K_{\ast}}(R)$ to $ {G_{\ast}}(R)$ factors through the groups $ K{V_{\ast}}(R)$. We also compute $ K{V_{\ast}}$ for the categories of faithful projectives and Azumaya algebras, generalizing results of Bass.


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DOI: https://doi.org/10.1090/S0002-9947-1981-0626494-7
Keywords: Karoubi-Villamayor $ K$-theory, exact category, symmetric monoidal category, infinite loop space
Article copyright: © Copyright 1981 American Mathematical Society