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 Τ we give a natural definition of groups K0(Τ) and K1(Τ) in terms of the universal determinant functor on Τ, and we show that Ki(Τ) ≅ Ki(ε) for i = 0 and 1 if Τ has a non-degenerate bounded t-structure with heart ε.
