On kernel modules of cotorsion pairs

Author(s):  
László Fuchs
Keyword(s):  
2014 ◽  
Vol 57 (2) ◽  
pp. 263-284 ◽  
Author(s):  
XIAOYAN YANG

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.


Author(s):  
Aimin Xu

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.


2017 ◽  
Vol 221 (6) ◽  
pp. 1249-1267 ◽  
Author(s):  
Daniel Bravo ◽  
Marco A. Pérez

2018 ◽  
Vol 156 ◽  
pp. 119-141 ◽  
Author(s):  
Huimin Chang ◽  
Yu Zhou ◽  
Bin Zhu

2019 ◽  
Vol 223 (5) ◽  
pp. 1833-1855
Author(s):  
Silvana Bazzoni ◽  
Marco Tarantino
Keyword(s):  

Author(s):  
Wenjing Chen ◽  
Zhongkui Liu

In this paper, we construct some model structures corresponding Gorenstein [Formula: see text]-modules and relative Gorenstein flat modules associated to duality pairs, Frobenius pairs and cotorsion pairs. By investigating homological properties of Gorenstein [Formula: see text]-modules and some known complete hereditary cotorsion pairs, we describe several types of complexes and obtain some characterizations of Iwanaga–Gorenstein rings. Based on some facts given in this paper, we find new duality pairs and show that [Formula: see text] is covering as well as enveloping and [Formula: see text] is preenveloping under certain conditions, where [Formula: see text] denotes the class of Gorenstein [Formula: see text]-injective modules and [Formula: see text] denotes the class of Gorenstein [Formula: see text]-flat modules. We give some recollements via projective cotorsion pair [Formula: see text] cogenerated by a set, where [Formula: see text] denotes the class of Gorenstein [Formula: see text]-projective modules. Also, many recollements are immediately displayed through setting specific complete duality pairs.


2011 ◽  
Vol 54 (3) ◽  
pp. 783-797 ◽  
Author(s):  
Gang Yang ◽  
Zhongkui Liu

AbstractWe show that if the given cotorsion pair $(\mathcal{A},\mathcal{B})$ in the category of modules is complete and hereditary, then both of the induced cotorsion pairs in the category of complexes are complete. We also give a cofibrantly generated model structure that can be regarded as a generalization of the projective model structure.


2010 ◽  
Vol 214 (5) ◽  
pp. 519-525 ◽  
Author(s):  
Riccardo Colpi ◽  
Francesca Mantese ◽  
Alberto Tonolo

2020 ◽  
Vol 115 (4) ◽  
pp. 379-389 ◽  
Author(s):  
Yu Liu
Keyword(s):  

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