Determinant functors on triangulated categories

Details Determinant functors on triangulated categories Determinant functors on triangulated categories

2006-10-13

arxiv.org/abs/math/0610435v1

Mathematics

Category Theory

39 pages

Scientific paper

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.

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