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Accessible Categories: The Foundations of Categorical Model Theory

Available Formats:
Electronic ISBN: 978-0-8218-7692-3
Product Code: CONM/104.E
List Price: $45.00 MAA Member Price:$40.50
AMS Member Price: $36.00 Click above image for expanded view Accessible Categories: The Foundations of Categorical Model Theory Available Formats:  Electronic ISBN: 978-0-8218-7692-3 Product Code: CONM/104.E  List Price:$45.00 MAA Member Price: $40.50 AMS Member Price:$36.00
• Book Details

Contemporary Mathematics
Volume: 1041990; 176 pp
MSC: Primary 03; 18;

Intended for category theorists and logicians familiar with basic category theory, this book focuses on categorical model theory, which is concerned with the categories of models of infinitary first order theories, called accessible categories. The starting point is a characterization of accessible categories in terms of concepts familiar from Gabriel-Ulmer's theory of locally presentable categories. Most of the work centers on various constructions (such as weighted bilimits and lax colimits), which, when performed on accessible categories, yield new accessible categories. These constructions are necessarily 2-categorical in nature; the authors cover some aspects of 2-category theory, in addition to some basic model theory, and some set theory. One of the main tools used in this study is the theory of mixed sketches, which the authors specialize to give concrete results about model theory. Many examples illustrate the extent of applicability of these concepts. In particular, some applications to topos theory are given.

Perhaps the book's most significant contribution is the way it sets model theory in categorical terms, opening the door for further work along these lines. Requiring a basic background in category theory, this book will provide readers with an understanding of model theory in categorical terms, familiarity with 2-categorical methods, and a useful tool for studying toposes and other categories.

• Chapters
• Introduction
• Chapter 1: Preliminaries
• Chapter 2: Accessible categories and functors
• Chapter 3: Sketches and logic
• Chapter 4: Sketching accessible categories
• Chapter 5: Limits and colimits of accessible categories
• Chapter 6: Limits and colimits in accessible categories
• References
• Index
• Glossary of notation
• Requests

Review Copy – for reviewers who would like to review an AMS book
Permission – for use of book, eBook, or Journal content
Accessibility – to request an alternate format of an AMS title
Volume: 1041990; 176 pp
MSC: Primary 03; 18;

Intended for category theorists and logicians familiar with basic category theory, this book focuses on categorical model theory, which is concerned with the categories of models of infinitary first order theories, called accessible categories. The starting point is a characterization of accessible categories in terms of concepts familiar from Gabriel-Ulmer's theory of locally presentable categories. Most of the work centers on various constructions (such as weighted bilimits and lax colimits), which, when performed on accessible categories, yield new accessible categories. These constructions are necessarily 2-categorical in nature; the authors cover some aspects of 2-category theory, in addition to some basic model theory, and some set theory. One of the main tools used in this study is the theory of mixed sketches, which the authors specialize to give concrete results about model theory. Many examples illustrate the extent of applicability of these concepts. In particular, some applications to topos theory are given.

Perhaps the book's most significant contribution is the way it sets model theory in categorical terms, opening the door for further work along these lines. Requiring a basic background in category theory, this book will provide readers with an understanding of model theory in categorical terms, familiarity with 2-categorical methods, and a useful tool for studying toposes and other categories.

• Chapters
• Introduction
• Chapter 1: Preliminaries
• Chapter 2: Accessible categories and functors
• Chapter 3: Sketches and logic
• Chapter 4: Sketching accessible categories
• Chapter 5: Limits and colimits of accessible categories
• Chapter 6: Limits and colimits in accessible categories
• References
• Index
• Glossary of notation
Review Copy – for reviewers who would like to review an AMS book
Permission – for use of book, eBook, or Journal content
Accessibility – to request an alternate format of an AMS title
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