Displaying similar documents to “Chain complexes and stable categories.”

Refining thick subcategory theorems

Sunil K. Chebolu (2006)

Fundamenta Mathematicae

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We use a K-theory recipe of Thomason to obtain classifications of triangulated subcategories via refining some standard thick subcategory theorems. We apply this recipe to the full subcategories of finite objects in the derived categories of rings and the stable homotopy category of spectra. This gives, in the derived categories, a complete classification of the triangulated subcategories of perfect complexes over some commutative rings. In the stable homotopy category of spectra we...

Extensions of covariantly finite subcategories revisited

Jing He (2019)

Czechoslovak Mathematical Journal

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Extriangulated categories were introduced by Nakaoka and Palu by extracting the similarities between exact categories and triangulated categories. A notion of homotopy cartesian square in an extriangulated category is defined in this article. We prove that in an extriangulated category with enough projective objects, the extension subcategory of two covariantly finite subcategories is covariantly finite. As an application, we give a simultaneous generalization of a result of X. W. Chen...