Motivic Measures through Waldhausen K-Theories

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In this paper we introduce the notion of a cdp-functor to a Waldhausen category. We show that such functors admit extensions that satisfy the excision property, to which we associate Euler-Poincaré characteristics that send the class of a proper scheme to the class of its image. As an application, we show that the Yoneda embedding gives rise to a monoidal proper-fibred Waldhausen category over Noetherian schemes of finite Krull dimensions, with canonical cdp-functors to its fibres.