A universal characterization of higher algebraic K-theory

In this paper we establish a universal characterization of higher algebraic K-theory in the setting of small stable 1-categories. Specifically, we prove that connective algebraic K-theory is the universal additive invariant, ie the universal functor with values in spectra which inverts Morita equivalences, preserves filtered colimits and satisfies Waldhausen's additivity theorem. Similarly, we prove that nonconnective algebraic K-theory is the universal localizing invariant, ie the universal functor that moreover satisfies the Thomason-Trobaugh-Neeman Localization Theorem.