Locally presentable and accessible categories

the long version

The concepts of a locally presentable category and an accessible category have turned out to be extremely 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. First the concepts of [lambda]-presentable objects, locally [lambda]-presentable categories, and [lambda]-accessible categories are discussed in detail. The authors go on to prove that Freyd's essentially algebraic categories are precisely the locally presentable categories. In the final chapter they treat some advanced topics in model theory. For researchers in category theory, algebra, computer science, and model theory, this book will be a necessary purchase.