%0 Journal Article %T The fundamental theorem via derived Morita invariance, localization, and A^1-homotopy invariance %A Goncalo Tabuada %J Mathematics %D 2011 %I arXiv %X We prove that every functor defined on dg categories, which is derived Morita invariant, localizing, and A^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. %U http://arxiv.org/abs/1103.5936v1