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a1-homotopy invariance

Journal of K-Theory (1)

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The fundamental theorem via derived Morita invariance, localization, and 1-homotopy invariance
Gonçalo Tabuada
Journal:

Journal of K-Theory / Volume 9 / Issue 3 / June 2012

Published online by Cambridge University Press:

24 May 2011, pp. 407-420

Print publication:

June 2012
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We prove that every functor defined on dg categories, which is derived Morita invariant, localizing, and 1-homotopy invariant, satisfies the fundamental theorem. As an application, we recover in a unified and conceptual way, Weibel and Kassel's fundamental theorems in homotopy algebraic K-theory, and periodic cyclic homology, respectively.