**CRM Proceedings & Lecture Notes**

Volume: 53;
2011;
426 pp;
Softcover

MSC: Primary 03; 18;

**Print ISBN: 978-0-8218-7281-9
Product Code: CRMP/53**

List Price: $130.00

AMS Member Price: $104.00

MAA Member Price: $117.00

**Electronic ISBN: 978-1-4704-1587-7
Product Code: CRMP/53.E**

List Price: $130.00

AMS Member Price: $104.00

MAA Member Price: $117.00

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# Models, Logics, and Higher-Dimensional Categories: A Tribute to the Work of Mihály Makkai

Share this page *Edited by *
*Bradd Hart; Thomas G. Kucera; Anand Pillay; Philip J. Scott; Robert A. G. Seely*

A co-publication of the AMS and Centre de Recherches Mathématiques

This book deals with the main themes in Mihály Makkai's research career: traditional model theory, categorical model theory and logics, and higher-dimensional category theory. Included are both research papers and survey papers, giving useful material for experts and students in these fields. Particularly valuable are papers that show how the techniques and understanding in one field can be productively applied to another; examples are the paper by Harnik, which explains how Shelah's \(T^{eq}\) construction (in model theory) is the same as the categorical notion of pretopos completion; the paper by Kamensky, which gives category-theoretic treatments of sophisticated notions from stability theory; and the paper by Prest relating categorical logic and the model theory of modules. These and other papers in this volume should make this a valuable resource for any mathematician interested in classical or categorical model theory or higher dimensional category theory.

Titles in this series are co-published with the Centre de Recherches Mathématiques.

#### Readership

Graduate students and research mathematicians interested in model theory, logic, and higher-dimensional category theory.

# Table of Contents

## Models, Logics, and Higher-Dimensional Categories: A Tribute to the Work of Mihaly Makkai

- Cover Cover11
- Title page iii4
- Contents v6
- Introduction vii8
- Mihály Makkai: A biographical note, with reminiscences ix10
- The number of countable models in categories of sheaves 112
- Pseudomonodacity and 2-stack completions 2940
- Purity and pure-injectivity for topological modules 5566
- Model theory vs. categorical logic: Two approaches to pretopos completion (a.k.a. 𝑇^{𝑒𝑞}) 7990
- The dialectica monad and its cousins 107118
- A categorical approach to internality 139150
- Computable structures of Scott rank 𝜔₁^{𝐶𝐾} 157168
- The Lorentz category in special relativity 169180
- A model-theoretic counterpart to Moishezon morphisms 177188
- Generic stability, regularity, and quasiminimality 189200
- Indexed Lawvere theories for local state 213224
- Model theory in additive categories 231242
- A derivation of Einstein’s vacuum field equations 245256
- An adventure into Hungarian word order with cyclic pregroups 263274
- No limit model in inaccessibles 277288
- The strict 𝜔-groupoid interpretation of type theory 291302
- Lax monoidal fibrations 341352
- Back Cover Back Cover1440