Applications of Cotorsion Pairs

By Henning Krause, Ø. Solberg. 2003

93 citations recorded by the source corpus.

Subfields: Geometry and Topology, Mathematical Physics, Statistical and Nonlinear Physics

View Paper: https://www.semanticscholar.org/paper/fd8b89d1613e269ba4997aac027f0c622b003cb5

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Citations in the corpus

Covers, precovers, and purity (2008, background): “3; the book [10] is a useful reference, but see also [2], [3], [7], [11], and [13].”
Homological and Homotopical Aspects of Torsion Theories (2007, background): “Note that there are slightly different definitions of cotorsion pairs which have appeared in the literature, see [97], [79].”
Thick subcategories and virtually Gorenstein algebras (2006, methodology): “Given any subcategory X of mod�, we denote by lim → X the full subcategory of Mod� consisting of all filtered colimits of modules in X. In [ 7, Theorem 2.4 ], it is shown that there are cotorsion pairs (lim − → C,lim → D) and (lim − → D,lim → E) for Mod�.”
Cohen-Macaulay modules, (co)torsion pairs and virtually Gorenstein algebras (2005, methodology): “If Γ is ak-algebra derived equivalent toΛ, then the stable categoryMod-Γ satisfies the Telescope Conjecture for torsion pairs such that the torsion class is triangu If Λ is self-injective and(X ,Y) is a cotorsion pair in Mod-Λ, then by a result o Krause–Solberg [45, Theorem 7.6] the subcategoriesX a”
Cotorsion pairs and model categories (2007, background): “In brief,a m odel category structureon an abelian category A thatrespectstheabelian structurein asim pleway isequivalenttotwocom patiblecom pletecotorsion pairs on A .”
Monomorphism categories, cotilting theory, and Gorenstein-projective modules (2011, background): “ t is an isomorphism. This completes the proof. 2.3. Proof of Theorem 2.1. By Corollary 1.4 and Lemma 2.3 Sn(A) is a resolving contravariantly ﬁnite subcategory in Tn(A)-mod. Then by Corollary 0.3 of [KS] (which asserts that a resolving contravariantly ﬁnite subcategory in A-mod is also covariantly ”
Cotorsion torsion triples and the representation theory of filtered hierarchical clustering (2019, background): “However, given a cotorsion torsion triple, the cotorsion pair is actually a cotorsion pair in the sense of [14], since T is closed under cosyzygies.”
The Tilting–Cotilting Correspondence (2017, background): “The following definitions are standard; see for instance [60], [63, §5] or [54, §§3 and 4] and the references there (the concept of a cotorsion pair goes back to [59] and have been extensively used in representation and module theory [35, 27]).”
On algebras of finite Cohen-Macaulay type (2011, background): “By a result of Krause-Solberg, see [57], pX,Yq extends to a cotorsion pair plimÝÑX, limÝÑYq in Mod-Λ.”