Determinant Functors on Triangulated Categories
نویسنده
چکیده
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 K0(T ) and K1(T ) in terms of the universal determinant functor on T , and we show that Ki(T ) ∼= Ki(E) for i = 0 and 1 if T has a non-degenerate bounded t-structure with heart E.
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