Stovicek, Jan

Locally well generated homotopy categories of complexes

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


Summary: 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 $\mathcal{B}= \textrm{Mod-}R$.

Mathematics Subject Classification

18G35, 18E30, 18E35, 16D90


compactly and well generated triangulated categories, complexes, pure semisimplicity