Adjoint functors and triangulated categories
范畴论
2007-08-20 v3 表示论
摘要
We give a construction of triangulated categories as quotients of exact categories where the subclass of objects sent to zero is defined by a triple of functors. This includes the cases of homotopy and stable module categories. These categories naturally fit into a framework of relative derived categories, and once we prove that there are decent resolutions of complexes, we are able to prove many familiar results in homological algebra.
引用
@article{arxiv.math/0601575,
title = {Adjoint functors and triangulated categories},
author = {Matthew Grime},
journal= {arXiv preprint arXiv:math/0601575},
year = {2007}
}
备注
20 pages. Added subsection on Transfer in the homotopy category, corrected typos (May 2006). Expanded to 20 pages, minor corrections, accepted for publication in Comm.in Alg. (August 2007)