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

Locally well generated homotopy categories of complexes