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