Determinant functors on triangulated categories
范畴论
2007-05-23 v1 K理论与同调
摘要
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.
引用
@article{arxiv.math/0610435,
title = {Determinant functors on triangulated categories},
author = {Manuel Breuning},
journal= {arXiv preprint arXiv:math/0610435},
year = {2007}
}
备注
39 pages