Locally well generated homotopy categories of complexes
Documenta mathematica, Tome 15 (2010), pp. 507-525.

Voir la notice de l'article dans Electronic Library of Mathematics

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 $\mathcal{B}= \textrm{Mod-}R$.
Classification : 18G35, 18E30, 18E35, 16D90
Mots-clés : compactly and well generated triangulated categories, complexes, pure semisimplicity 
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     author = {Stovicek, Jan},
     title = {Locally well generated homotopy categories of complexes},
     journal = {Documenta mathematica},
     pages = {507--525},
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     volume = {15},
     year = {2010},
     language = {en},
     url = {https://geodesic-test.mathdoc.fr/item/DOCMA_2010__15__a20/}
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Stovicek, Jan. Locally well generated homotopy categories of complexes. Documenta mathematica, Tome 15 (2010), pp. 507-525. https://geodesic-test.mathdoc.fr/item/DOCMA_2010__15__a20/