Preface Chapter 1 Preliminaries 1.1 Some Basic Concepts about Equivalences 1.2 Grothendieck Categories 1.3 The Morita Theory of Equivalences 1.4 Basic Concepts of Coalgebras and Comodules Chapter 2 Fuller's Equivalence 2.1 Definitions and Basic Facts 2.2 Fuller's Equivalence Theorems 2.3 The Properties of Quasi-progenerators Chapter 3 Equivalences Studied by Sato and Azumaya 3.1 Sato's Equivalences 3.2 Azumaya's Equivalences Chapter 4 Classical Tilting Modules and Equivalences 4.1 Tilting Theorem for Classical Tilting Modules 4.2 The Characterizations of Classical Tilting Modules 4.3 Generalized Classical Tilting Modules Chapter 5 Equivalences Induced by*-Modules 5.1 Representable Equivalences of Subcategories 5.2 Every*-Module Is Finitely Generated 5.3 Some Characterizations of*-Modules Chapter 6 Applications of the Theories for *.Modules 6.1 Some Characterizations of Classical Tilting Modules by*-Modules 6.2 Equivalences Between Projective.Injective Modules 6.3 Examples 6.4 Relations Between Some Classes Involved *-Modules 6.5 Recent Developments about the Tilting Theory Chapter 7 Morita-Like Equiralence 7.1 Morita—Like Equivalence and XST—Rings 7.2 Morita Theory for XST-Rings Chapter 8 A Characterization for Comodule Category 8.1 Two Functors h＿c（-，-）and-□C＿ 8.2 Locally Finite Abelian Categories 8.3 A Characterization of Comodules Categories Chapter 9 Morita-Takeuchi Equivalence 9.1 Morita-Takeuchi Pre-equivalence Data 9.2 Constructing a Morita-Takeuchi Equivalence Chapter 10 Strongly Equivalences 10.1 Morita’s Theorem for Coalgebras 10.2 Lin’s Theorem for Strong Equivalence 10.3 Some Improvements for Strongly Equivalence 10.4 Examples Chapter 11 QcF and Conoetherian Coalgebras 11.1 Introduction 1 1.2 Some Characterizations for QcF-coalgebras 11.3 Conoetherian Coalgebras Chapter 12 Equivalences and Tilting Comodules 12.1 Co-Noetherian Coalgebras 12.2 Some Basic Properties for Co-Hom 12.3 Equivalences and Classical Tilting Comodules Chapter 13 Properties Preserved by Equivalences 13.1 Some Basic Propositions Preserved by M-T Equivalence 13.2 Propositions Preserved by Strongly Equivalence Chapter 14 A List of Some Open Problems Bibliography Index
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