Locally well generated homotopy categories of complexes

  • Jan Stovicek

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Abstract

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

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Jan Stovicek, Locally well generated homotopy categories of complexes. Doc. Math. 15 (2010), pp. 507–525

DOI 10.4171/DM/304