The concepts of a locally presentable category and an accessible
category have turned out to be useful in formulating connections
between universal algebra, model theory, logic and computer
science. The aim of this book is to provide an exposition of both
the theory and the applications of these categories at a level
accessible to graduate students. Firstly the properties of
l-presentable objects, locally l-presentable categories, and
l-accessible categories are discussed in detail, and the
equivalence of accessible and sketchable categories is proved. The
authors go on to study categories of algebras and prove that
Freyd's essentially algebraic categories are precisely the locally
presentable categories. In the final chapters they treat some
topics in model theory and some set theoretical aspects. For
researchers in category theory, algebra, computer science, and
model theory, this book will be a necessary purchase.
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