Determinant functors on triangulated categories

We study determinant functors which are defined on a triangulated category and take values in a Picard category. The two main results are the existence of a universal determinant functor for every small triangulated category, and a comparison theorem for determinant functors on a triangulated category with a non-degenerate bounded t-structure and determinant functors on its heart. For a small triangulated category T we give a natural definition of groups K-0(T) and K-1(T) in terms of the universal determinant functor on T, and we show that K-i(T) congruent to K-i(epsilon) for i = 0 and 1 if T has a non-degenerate bounded t-structure with heart epsilon.