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• W3104589427 abstract "Let $Rto A$ be a homomorphism of associative rings, and let $(mathcal F,mathcal C)$ be a hereditary complete cotorsion pair in $Rmathsf{-Mod}$. Let $(mathcal F_A,mathcal C_A)$ be the cotorsion pair in $Amathsf{-Mod}$ in which $mathcal F_A$ is the class of all left $A$-modules whose underlying $R$-modules belong to $mathcal F$. Assuming that the $mathcal F$-resolution dimension of every left $R$-module is finite and the class $mathcal F$ is preserved by the coinduction functor $operatorname{Hom}_R(A,-)$, we show that $mathcal C_A$ is the class of all direct summands of left $A$-modules finitely (co)filtered by $A$-modules coinduced from $R$-modules from $mathcal C$. Assuming that the class $mathcal F$ is closed under countable products and preserved by the functor $operatorname{Hom}_R(A,-)$, we prove that $mathcal C_A$ is the class of all direct summands of left $A$-modules cofiltered by $A$-modules coinduced from $R$-modules from $mathcal C$, with the decreasing filtration indexed by the natural numbers. A combined result, based on the assumption that countable products of modules from $mathcal F$ have finite $mathcal F$-resolution dimension bounded by $k$, involves cofiltrations indexed by the ordinal $omega+k$. The dual results also hold, provable by the same technique going back to the author's monograph on semi-infinite homological algebra arXiv:0708.3398. In addition, we discuss the $n$-cotilting and $n$-tilting cotorsion pairs, for which we obtain better results using a suitable version of a classical Bongartz-Ringel lemma. As an illustration of the main results of the paper, we consider certain cotorsion pairs related to the contraderived and coderived categories of curved DG-modules." @default.
• W3104589427 created "2020-11-23" @default.
• W3104589427 creator A5049263004 @default.
• W3104589427 date "2023-02-16" @default.
• W3104589427 modified "2023-09-27" @default.
• W3104589427 title "An explicit self-dual construction of complete cotorsion pairs in the relative context" @default.
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• W3104589427 doi "https://doi.org/10.4171/rsmup/118" @default.
• W3104589427 hasPublicationYear "2023" @default.
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