Determinant functors on triangulated categories

Abstract 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 categoryΤwe give a natural definition of groupsK0(Τ) andK1(Τ) in terms of the universal determinant functor on Τ, and we show thatKi(Τ) ≅Ki(ε) fori= 0 and 1 ifΤhas a non-degenerate bounded t-structure with heartε.