Cotorsion pairs and model categories

Interactions between Homotopy Theory and Algebra - Contemporary Mathematics ◽

10.1090/conm/436/08413 ◽

2007 ◽

pp. 277-296 ◽

Cited By ~ 10

Author(s):

Mark Hovey

Keyword(s):

Model Categories ◽

Cotorsion Pairs

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On the construction of functorial factorizations for model categories

Algebraic & Geometric Topology ◽

10.2140/agt.2013.13.1089 ◽

2013 ◽

Vol 13 (2) ◽

pp. 1089-1124 ◽

Cited By ~ 5

Author(s):

Tobias Barthel ◽

Emily Riehl

Keyword(s):

Model Categories

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Functorial Factorizations in the Category of Model Categories

Applied Categorical Structures ◽

10.1007/s10485-021-09636-y ◽

2021 ◽

Author(s):

Hugo Bacard

Keyword(s):

Model Categories

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MODEL STRUCTURES ON TRIANGULATED CATEGORIES

Glasgow Mathematical Journal ◽

10.1017/s0017089514000299 ◽

2014 ◽

Vol 57 (2) ◽

pp. 263-284 ◽

Cited By ~ 5

Author(s):

XIAOYAN YANG

Keyword(s):

Proper Class ◽

Triangulated Category ◽

Triangulated Categories ◽

General Study ◽

Proper Class Of Triangles ◽

Cotorsion Pairs ◽

One To One ◽

The Relationship ◽

Model Structures

AbstractWe define model structures on a triangulated category with respect to some proper classes of triangles and give a general study of triangulated model structures. We look at the relationship between these model structures and cotorsion pairs with respect to a proper class of triangles on the triangulated category. In particular, we get Hovey's one-to-one correspondence between triangulated model structures and complete cotorsion pairs with respect to a proper class of triangles. Some applications are given.

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New model structures and projective (injective) cotorsion pairs

Journal of Algebra and Its Applications ◽

10.1142/s0219498823500366 ◽

2021 ◽

Author(s):

Aimin Xu

Keyword(s):

Positive Integer ◽

Triangulated Categories ◽

Model Structure ◽

Cotorsion Pair ◽

Flat Dimension ◽

Gorenstein Projective Module ◽

Chain Complexes ◽

Cotorsion Pairs ◽

Gorenstein Injective ◽

Model Structures

Let [Formula: see text] be either the category of [Formula: see text]-modules or the category of chain complexes of [Formula: see text]-modules and [Formula: see text] a cofibrantly generated hereditary abelian model structure on [Formula: see text]. First, we get a new cofibrantly generated model structure on [Formula: see text] related to [Formula: see text] for any positive integer [Formula: see text], and hence, one can get new algebraic triangulated categories. Second, it is shown that any [Formula: see text]-strongly Gorenstein projective module gives rise to a projective cotorsion pair cogenerated by a set. Finally, let [Formula: see text] be an [Formula: see text]-module with finite flat dimension and [Formula: see text] a positive integer, if [Formula: see text] is an exact sequence of [Formula: see text]-modules with every [Formula: see text] Gorenstein injective, then [Formula: see text] is injective.

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