Adjoint functors and triangulated categories

Details Adjoint functors and triangulated categories Adjoint functors and triangulated categories

2006-01-24

arxiv.org/abs/math/0601575v3

Mathematics

Category Theory

20 pages. Added subsection on Transfer in the homotopy category, corrected typos (May 2006). Expanded to 20 pages, minor corre

Scientific paper

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.

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