On Torsion Theories, Weight and t-Structures in Triangulated Categories

2019 ◽  
Vol 52 (1) ◽  
pp. 19-29 ◽  
Author(s):  
M. V. Bondarko ◽  
S. V. Vostokov
Keyword(s):  
Triangulated Categories ◽  
Torsion Theories

Prestressed Concrete Tests Compared With Torsion Theories

PCI Journal ◽  
1985 ◽  
Vol 30 (5) ◽  
pp. 96-127 ◽  
Author(s):  
Arthur E. McMullen ◽  
Wael M. EI-Degwy
Keyword(s):  
Prestressed Concrete ◽  
Torsion Theories

scholarly journals Recollements, comma categories and morphic enhancements

2021 ◽  
pp. 1-25
Author(s):  
Xiao-Wu Chen ◽  
Jue Le
Keyword(s):  
Module Category ◽  
Triangulated Category ◽  
Triangulated Categories ◽  
Comma Category ◽  
The Right ◽  
Projective Lines ◽  
Triangle Functor

For each recollement of triangulated categories, there is an epivalence between the middle category and the comma category associated with a triangle functor from the category on the right to the category on the left. For a morphic enhancement of a triangulated category $\mathcal {T}$ , there are three explicit ideals of the enhancing category, whose corresponding factor categories are all equivalent to the module category over $\mathcal {T}$ . Examples related to inflation categories and weighted projective lines are discussed.

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.

scholarly journals Grade of Ideals with Respect to Torsion Theories

2013 ◽  
Vol 41 (9) ◽  
pp. 3224-3240
Author(s):  
Mohsen Asgharzadeh ◽  
Massoud Tousi
Keyword(s):  
Torsion Theories

scholarly journals Protoadditive functors, derived torsion theories and homology

2015 ◽  
Vol 219 (8) ◽  
pp. 3629-3676 ◽  
Author(s):  
Tomas Everaert ◽  
Marino Gran
Keyword(s):  
Torsion Theories

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 On graded centres and block cohomology

2009 ◽  
Vol 52 (2) ◽  
pp. 489-514 ◽  
Author(s):  
Markus Linckelmann
Keyword(s):  
Triangulated Categories ◽  
Nilpotent Ideal ◽  
Stable Elements ◽  
Block Algebra

AbstractWe extend the group theoretic notions of transfer and stable elements to graded centres of triangulated categories. When applied to the centre Z*(Db(B) of the derived bounded category of a block algebra B we show that the block cohomology H*(B) is isomorphic to a quotient of a certain subalgebra of stable elements of Z*(Db(B)) by some nilpotent ideal, and that a quotient of Z*(Db(B)) by some nilpotent ideal is Noetherian over H*(B).

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