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A Morita type theorem for a sort of quotient categories

Simion Breaz (2005)

Czechoslovak Mathematical Journal

We consider the quotient categories of two categories of modules relative to the Serre classes of modules which are bounded as abelian groups and we prove a Morita type theorem for some equivalences between these quotient categories.

Explicit cogenerators for the homotopy category of projective modules over a ring

Amnon Neeman (2011)

Annales scientifiques de l'École Normale Supérieure

Let R be a ring. In two previous articles [12, 14] we studied the homotopy category 𝐊 ( R - Proj ) of projective R -modules. We produced a set of generators for this category, proved that the category is 1 -compactly generated for any ring R , and showed that it need not always be compactly generated, but is for sufficiently nice R . We furthermore analyzed the inclusion j ! : 𝐊 ( R - Proj ) 𝐊 ( R - Flat ) and the orthogonal subcategory 𝒮 = 𝐊 ( R - Proj ) . And we even showed that the inclusion 𝒮 𝐊 ( R - Flat ) has a right adjoint; this forces some natural map to be an equivalence...

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