Contemporary Mathematics 1990; 176 pp; softcover Volume: 104 Reprint/Revision History: reprinted 1991 ISBN10: 082185111X ISBN13: 9780821851111 List Price: US$45 Member Price: US$36 Order Code: CONM/104
 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 GabrielUlmer'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 2categorical in nature; the authors cover some aspects of 2category 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 2categorical methods, and a useful tool for studying toposes and other categories. Table of Contents  Preliminaries
 \(\kappa\)filtered colimits
 \(\kappa\)flat functors
 Accessible categories and functors
 \(\kappa\)accessible categories
 Small categories and accessibility
 Raising the index of accessibility
 Accessible functors
 An equivalent definition of accessibility
 Sketches and logic
 Sketches
 Logic
 The downward LöwenheimSkolem theorem
 Examples
 Sketching accessible categories
 Preliminaries on \(2\)categories
 The canonical sketch associated with a \(\kappa\)accessible category
 Small sketches for an accessible category
 Diagrams of accessible categories and diagrams of sketches
 Axiomatizing an accessible subcategory
 Limits and colimits of accessible categories
 Colimits of sketches and limits of accessible categories
 Some results concerning Grothendieck toposes
 Accessible fibrations
 Lax colimits of accessible categories
 The powerful image of an accessible functor
 Limits and colimits in accessible categories
 Completeness and cocompleteness in accessible categories
 Models of a sketch in an accessible category
 Detectability of colimits
 Completing an accessible category
