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Homological and Homotopical Aspects of Torsion Theories (Paperback) Loot Price: R1,638
Discovery Miles 16 380
Homological and Homotopical Aspects of Torsion Theories (Paperback): Apostolos Beligiannis, Idun Reiten
Homological and Homotopical Aspects of Torsion Theories (Paperback): Apostolos Beligiannis, Idun Reiten

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Homological and Homotopical Aspects of Torsion Theories (Paperback)

Apostolos Beligiannis, Idun Reiten

Series: Memoirs of the American Mathematical Society, No. 188

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Loot Price R1,638 Discovery Miles 16 380 | Repayment Terms: R152 pm x 12*

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In this paper the authors investigate homological and homotopical aspects of a concept of torsion which is general enough to cover torsion and cotorsion pairs in abelian categories, $t$-structures and recollements in triangulated categories, and torsion pairs in stable categories. The proper conceptual framework for this study is the general setting of pretriangulated categories, an omnipresent class of additive categories which includes abelian, triangulated, stable, and more generally (homotopy categories of) closed model categories in the sense of Quillen, as special cases. The main focus of their study is on the investigation of the strong connections and the interplay between (co)torsion pairs and tilting theory in abelian, triangulated and stable categories on one hand, and universal cohomology theories induced by torsion pairs on the other hand. These new universal cohomology theories provide a natural generalization of the Tate-Vogel (co)homology theory. The authors also study the connections between torsion theories and closed model structures, which allow them to classify all cotorsion pairs in an abelian category and all torsion pairs in a stable category, in homotopical terms. For instance they obtain a classification of (co)tilting modules along these lines. Finally they give torsion theoretic applications to the structure of Gorenstein and Cohen-Macaulay categories, which provide a natural generalization of Gorenstein and Cohen-Macaulay rings.

General

Imprint: American Mathematical Society
Country of origin: United States
Series: Memoirs of the American Mathematical Society, No. 188
Release date: May 2007
Authors: Apostolos Beligiannis • Idun Reiten
Dimensions: 17mm (H)
Format: Paperback
Pages: 207
ISBN-13: 978-0-8218-3996-6
Barcode: 9780821839966
Categories: Books > Science & Mathematics > Mathematics > Algebra > Groups & group theory
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Books > Science & Mathematics > Mathematics > Topology
Books > Science & Mathematics > Mathematics > Topology > General
LSN: 0-8218-3996-9

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