Locally Presentable and Accessible Categories

Erscheinungsjahr 2004
ISBN: 978-0-521-42261-1
Verlag: Cambridge University Press

Buch, Englisch, Band 189, 329 Seiten, Format (B × H): 152 mm x 229 mm, Gewicht: 540 g

Reihe: London Mathematical Society Lecture Note Series

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.

Autoren/Hrsg.

Rosicky, Jiri

Adamek, J.

Rosicky, J.

Fachgebiete

• Mathematik | Informatik Mathematik Mathematik Allgemein Mathematische Logik

Inhaltsverzeichnis

Preliminaries; 1. Locally presentable categories; 2. Accessible categories; 3. Algebraic categories; 4. Injectivity classes; 5. Categories of models; 6. Vopenka's principle; Appendix: Large cardinals; Open problems.