Non-connective K- and Nil-spectra of additive categorie

We present an elementary construction of the non-connective algebraic K-theory spectrum associated to an additive category following the contracted functor approach due to Bass. It comes with a universal property that easily allows us to identify it with other constructions, for instance with the one of Pedersen-Weibel in terms of Z^i-graded objects and bounded homomorphisms.