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Abelian Model Category Theory
出版済み 3-5週間でお届けいたします。
アーベルモデル圏論 Series: Cambridge Studies in Advanced Mathematics Author: Gillespie, James (Ramapo College of New Jersey) Publisher: Cambridge University Press ISBN: 9781009449465 Cover: HARDCOVER Date: 2025年01月 DESCRIPTION アーベルモデル圏は最新の研究においてさらに大きな注目を集めています。明確な図形的証明を盛り込んだ本書は、アーベルおよび完全モデル圏の基礎を初歩から取り上げます。代数、トポロジー、表現論、圏論の研究者と大学院生に必要なすべてが揃った入門書です。 Offering a unique resource for advanced graduate students and researchers, this book treats the fundamentals of Quillen model structures on abelian and exact categories. Building the subject from the ground up using cotorsion pairs, it develops the special properties enjoyed by the homotopy category of such abelian model structures. A central result is that the homotopy category of any abelian model structure is triangulated and characterized by a suitable universal property - it is the triangulated localization with respect to the class of trivial objects. The book also treats derived functors and monoidal model categories from this perspective, showing how to construct tensor triangulated categories from cotorsion pairs. For researchers and graduate students in algebra, topology, representation theory, and category theory, this book offers clear explanations of difficult model category methods that are increasingly being used in contemporary research. * Clearly explains abstract concepts including an abundance of diagrammatic proofs * Uses an accessible approach, developing the fundamentals of abelian model categories from the cotorsion pair perspective * Develops theory within the more general setting of Quillen exact categories, making results more widely applicable TABLE OF CONTENTS Introduction and main examples: 1. Additive and exact categories 2. Cotorsion pairs 3. Stable categories from cotorsion pairs 4. Hovey triples and abelian model structures 5. The homotopy category of an abelian model structure 6. The triangulated homotopy category 7. Derived functors and abelian monoidal model structures 8. Hereditary model structures 9. Constructing complete cotorsion pairs 10. Abelian model structures on chain complexes 11. Mixed model structures and examples 12. Cofibrant generation and well-generated homotopy categories A. Hovey's correspondence for general exact categories B. Right and left homotopy relations C. Bibliographical notes References Index.
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