The fundamental theorem via derived Morita invariance, localization, and A1-homotopy invariance
Abstract
We prove that every functor defined on dg categories, which is derived Morita invariant, localizing, and A1-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.
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