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. 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.
General
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