E-Book Overview
This book provides a unified approach to much of the theories of equivalence and duality between categories of modules that has transpired over the last 45 years. More recently, many authors (including the authors of this book) have investigated relationships between categories of modules over a pair of rings that are induced by both covariant and contravariant representable functors, in particular, by tilting and cotilting theories. Collecting and unifying the basic results of these investigations with innovative and easily understandable proofs, the authors' provide an aid to further research on this central topic in abstract algebra.
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EQUIVALENCE AND DUALITY FOR MODULE CATEGORIES (with Tilting and Cotilting for Rings)
This book provides a unified approach to many of the theories of equivalence and duality between categories of modules that have transpired over the last 45 years. In particular, during the past dozen or so years many authors (including the authors of this book) have investigated relationships between categories of modules over a pair of rings that are induced by both covariant and contravariant representable functors, in particular by tilting and cotilting theories. By here collecting and unifying the basic results of these investigations with innovative and easily understandable proofs, the authors’ aim is to provide an aid to further research in this central topic in abstract algebra and a reference for all whose research lies in this field. Robert R. Colby is Professor Emeritus at the University of Hawaii and Independent Scholar at the University of Iowa. Kent R. Fuller is a professor of mathematics at the University of Iowa.
CAMBRIDGE TRACTS IN MATHEMATICS General Editors
` W. FULTON, A. KATOK, F. KIRWAN, B. BOLLOBAS, P. SARNAK, B. SIMON
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Equivalence and Duality for Module Categories (with T