scholarly journals Cotorsion pairs induced by duality pairs

2009 ◽  
Vol 1 (4) ◽  
pp. 621-633 ◽  
Author(s):  
Henrik Holm ◽  
Peter Jørgensen
Keyword(s):  
Duality Pairs ◽  
Cotorsion Pairs

Model structures, recollements and duality pairs

2021 ◽  
Author(s):  
Wenjing Chen ◽  
Zhongkui Liu
Keyword(s):  
Projective Modules ◽  
Cotorsion Pair ◽  
Gorenstein Rings ◽  
Injective Modules ◽  
Flat Modules ◽  
Duality Pairs ◽  
Cotorsion Pairs ◽  
Gorenstein Flat ◽  
Model Structures

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.

scholarly journals On Infinite–finite Duality Pairs of Directed Graphs

Order ◽  
2012 ◽  
Vol 30 (3) ◽  
pp. 807-819
Author(s):  
Péter L. Erdős ◽  
Claude Tardif ◽  
Gábor Tardos
Keyword(s):  
Directed Graphs ◽  
Duality Pairs

scholarly journals MODEL STRUCTURES ON TRIANGULATED CATEGORIES

2014 ◽  
Vol 57 (2) ◽  
pp. 263-284 ◽  
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.

New model structures and projective (injective) cotorsion pairs

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.

scholarly journals Finiteness conditions and cotorsion pairs

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

Cotorsion pairs in cluster categories of type A∞∞

2018 ◽  
Vol 156 ◽  
pp. 119-141 ◽  
Author(s):  
Huimin Chang ◽  
Yu Zhou ◽  
Bin Zhu
Keyword(s):  
Type A ◽  
Cluster Categories ◽  
Cotorsion Pairs

scholarly journals Recollements from cotorsion pairs

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

Relative FP-gr-injective and gr-flat modules

2018 ◽  
Vol 28 (06) ◽  
pp. 959-977 ◽  
Author(s):  
Tiwei Zhao ◽  
Zenghui Gao ◽  
Zhaoyong Huang
Keyword(s):  
Graded Modules ◽  
Flat Modules ◽  
Duality Pairs ◽  
Coherent Rings ◽  
Flat Cover ◽  
Finitely Presented

Let [Formula: see text] be an integer. We introduce the notions of [Formula: see text]-FP-gr-injective and [Formula: see text]-gr-flat modules. Then we investigate the properties of these modules by using the properties of special finitely presented graded modules and obtain some equivalent characterizations of [Formula: see text]-gr-coherent rings in terms of [Formula: see text]-FP-gr-injective and [Formula: see text]-gr-flat modules. Moreover, we prove that the pairs (gr-[Formula: see text], gr-[Formula: see text]) and (gr-[Formula: see text], gr-[Formula: see text]) are duality pairs over left [Formula: see text]-coherent rings, where gr-[Formula: see text] and gr-[Formula: see text] denote the subcategories of [Formula: see text]-FP-gr-injective left [Formula: see text]-modules and [Formula: see text]-gr-flat right [Formula: see text]-modules respectively. As applications, we obtain that any graded left (respectively, right) [Formula: see text]-module admits an [Formula: see text]-FP-gr-injective (respectively, [Formula: see text]-gr-flat) cover and preenvelope.

Cotorsion pairs and model structures on Ch(R)

2011 ◽  
Vol 54 (3) ◽  
pp. 783-797 ◽  
Author(s):  
Gang Yang ◽  
Zhongkui Liu
Keyword(s):  
Model Structure ◽  
Cotorsion Pair ◽  
Projective Model ◽  
Cotorsion Pairs ◽  
Category Of Modules ◽  
The Given ◽  
Model Structures

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.

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