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Adjoint functors and triangulated categories

Matthew Grime
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Abstract

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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Matthew Grime. 2007-08-20. Adjoint functors and triangulated categories. https://arxiv.org/abs/math/0601575

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