Approximations and adjoints in homotopy categories

Details Approximations and adjoints in homotopy categories Approximations and adjoints in homotopy categories

2010-05-03

arxiv.org/abs/1005.0209v2

Mathematics

Category Theory

15 pages, added some remarks, another description of the pure derived category of a module category, and an example

Scientific paper

We provide a criterion for the existence of right approximations in cocomplete additive categories; it is a straightforward generalisation of a result due to El Bashir. This criterion is used to construct adjoint functors in homotopy categories. Applications include the study of (pure) derived categories. For instance, it is shown that the pure derived category of any module category is compactly generated.

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