  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)=K_i(E) for i=0 and 1 if T has a non-degenerate bounded t-structure with
heart E.
