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

TL;DR

This paper introduces an elementary construction of non-connective algebraic K-theory spectra for additive categories, utilizing Bass's contracted functor approach, and establishes its universal property for comparison with existing models.

Contribution

It provides a new, elementary construction of non-connective K-theory spectra with a universal property, simplifying comparisons with other formulations.

Findings

Construction aligns with Pedersen-Weibel's model

Universal property facilitates identification with other spectra

Simplifies the understanding of non-connective K-theory

Abstract

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.