Locally Presentable and Accessible Categories
Locally Presentable and Accessible Categories
J. Rosicky
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(C) USDThe 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.
- Contains many applications of theory to computer science
- The only comprehensive work on this subject in English
Reviews & endorsements
"...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
Product details
March 2011Adobe eBook Reader
9780511892615
0 pages
0kg
This ISBN is for an eBook version which is distributed on our behalf by a third party.
Table of Contents
- 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.
