Locally Presentable and Accessible Categories

ISBN-13: 9780521422611 / Angielski / Miękka / 1994 / 332 str.

Jiri Adamek; Jiri Rosicky; J. Adamek

Opis

The concepts of a locally presentable category and an accessible category are 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. The concepts of lambda-presentable objects, locally lambda-presentable categories, and lambda-accessible categories are discussed in detail. The authors 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.

Recenzje

"...the authors have taken the indicated material, organized it effectively, written a very lucid, readable development of it in 280 pages, and added helpful historical remarks to each chapter and a brief appendix on large cardinals. There are some novel results...most notably a significant improvement of the Gabriel-Ulmer theorem on "local generation" of locally presentable categories." J.R. Isbell, Mathematical Reviews

Spis treści

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.