**Contemporary Mathematics**

Volume: 104;
1990;
176 pp;
Softcover

MSC: Primary 03; 18;

Print ISBN: 978-0-8218-5111-1

Product Code: CONM/104

List Price: $45.00

Individual Member Price: $36.00

**Electronic ISBN: 978-0-8218-7692-3
Product Code: CONM/104.E**

List Price: $45.00

Individual Member Price: $36.00

# Accessible Categories: The Foundations of Categorical Model Theory

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*R Paré; Michael Makkai*

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.

#### Table of Contents

# Table of Contents

## Accessible Categories: The Foundations of Categorical Model Theory

- Contents vii8 free
- Introduction 110 free
- Chapter 1: Preliminaries 1120
- Chapter 2: Accessible categories and functors 1726
- Chapter 3: Sketches and logic 3948
- Chapter 4: Sketching accessible categories 6776
- Chapter 5: Limits and Colimits of accessible categories 97106
- Chapter 6: Limits and Colimits in accessible categories 141150
- References 165174
- Index 167176
- Glossary of notation 173182