Abelian Model Category Theory
暫譯: 阿貝爾模型範疇理論

Gillespie, James

  • 出版商: Cambridge
  • 出版日期: 2025-01-02
  • 售價: $3,020
  • 貴賓價: 9.5$2,869
  • 語言: 英文
  • 頁數: 436
  • 裝訂: Hardcover - also called cloth, retail trade, or trade
  • ISBN: 100944946X
  • ISBN-13: 9781009449465
  • 海外代購書籍(需單獨結帳)

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商品描述

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.

商品描述(中文翻譯)

本書為進階研究生和研究人員提供了一個獨特的資源,探討了在阿貝爾類別和精確類別上的 Quillen 模型結構的基本原理。該書從基礎開始,利用共扭對(cotorsion pairs)來構建主題,發展了這些阿貝爾模型結構的同倫類別所享有的特殊性質。一個核心結果是,任何阿貝爾模型結構的同倫類別都是三角形的,並且由適當的普遍性質來特徵化——它是相對於平凡物件類別的三角形局部化。該書還從這一視角探討了導出函子和單體模型類別,展示了如何從共扭對構建張量三角形類別。對於代數、拓撲、表示理論和類別理論的研究人員和研究生來說,本書提供了對當前研究中越來越多使用的困難模型類別方法的清晰解釋。