Locally well generated homotopy categories of complexes

Details Locally well generated homotopy categories of complexes Locally well generated homotopy categories of complexes

2008-10-31

arxiv.org/abs/0810.5684v2

Doc. Math. 15 (2010), 507-525

Mathematics

Category Theory

17 pages, minor changes, final version, to appear in Documenta Mathematica

Scientific paper

We show that the homotopy category of complexes K(B) over any finitely accessible additive category B is locally well generated. That is, any localizing subcategory L in K(B) which is generated by a set is well generated in the sense of Neeman. We also show that K(B) itself being well generated is equivalent to B being pure semisimple, a concept which naturally generalizes right pure semisimplicity of a ring R for B = Mod-R.

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