We give a construction of triangulated categories as quotients of exact categories where the subclass of objects sent to zero is defined by a tripe 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.
|Translated title of the contribution||Adjoint functors and triangulated categories|
|Publisher||Cornell University Press|
|Publication status||Published - 20 Aug 2007|