Cotorsion pairs, model category structures, and representation theory

By Mark Hovey. 2002

309 citations recorded by the source corpus.

Subfields: Algebra and Number Theory, Geometry and Topology, Mathematical Physics

View Paper: https://www.semanticscholar.org/paper/d1ec56174e6a039f5bfd7cb08f0a11bb0f27ae57

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In Algebra and Number Theory

In Geometry and Topology

In Mathematical Physics

Citations in the corpus

Extriangulated categories, Hovey twin cotorsion pairs and model structures (2019, background): “We give a bijective correspondence between some pairs of cotorsion pairs which we call Hovey twin cotorsion pairs, and admissible model structures. As a consequence, these model structures relate certain localizations with certain ideal quotients, via the homotopy category which can be given a trian”
Model category structures arising from Drinfeld vector bundles (2009, methodology): “First, the results of [ 20, Section 5 ] guarantee that the weak equivalences of our model structure are the homology isomorphisms.”
On exact categories and applications to triangulated adjoints and model structures (2010, methodology): “ty (in the sense of [48, 8.2.1]) at their disposal. Their workaround relied on the fact that certain classes of complexes of sheaves were precovering. (2) Following a program described in [30], Hovey [29] and Gillespie [18, 19, 20] constructed monoidal model structures on categories of complexes of ”
Almost free modules and Mittag-Leffler conditions (2009, methodology): “So unlike the classes of all projective and flat modules, the class D does not admit the homotopy theory tools developed recently by Hovey [ 25 ].”
On Ding injective, Ding projective, and Ding flat modules and complexes (2015, background): “othendieck categories have enough injectives it turns out that such a cotorsion pair is equivalent to an injective model structure on G. By this we mean the model structure is abelian in the sense of [Hov02] and all objects are coﬁbrant. The ﬁbrant objects in this case are exactly Fand the trivial o”
Models for singularity categories (2012, background): “hat an abelian model structure is determined by the triple of coﬁbrant, weakly trivial and ﬁbrant objects. The question which such triples actually give rise to abelian model structures was solved in [Hov02] in terms of complete cotorsion pairs: Deﬁnition 1.1.7 ([Hov02, Deﬁnition 2.3]). For an abeli”
Gorenstein categories and Tate cohomology on projective schemes (2007, methodology): “Proof. This is just an application of [ 23, Theorem 2.2 ], (also see [2 3, Theorem 8.6]).”
Exact model categories, approximation theory, and cohomology of quasi-coherent sheaves (2013, methodology): “The idea here is due to Hovey [42].”
Homotopy Equivalences induced by Balanced Pairs (2008, unknown): “... full subcategory X, set X ⊥ = {M ∈ A | Ext 1(X,M) = 0 for all X ∈ X } and ⊥ X = {M ∈ A | Ext 1(M,X) = 0 for all X ∈ X }. A pair (X, Y) of full subcategories of A is called a cotorsion pair provided that X = ⊥ Y and Y = X ⊥ . The cotorsion pair (X, Y) is said to be complete provided that for each”
Cotorsion pairs and model categories (2007, methodology): “LetC denote the classofco brantobjects,F the classof brantobjects,and W the class ofacyclic objects (those thatare weakly equivalentto 0).”