**Contemporary Mathematics**

Volume: 30;
1984;
307 pp;
Softcover

MSC: Primary 18;

Print ISBN: 978-0-8218-5032-9

Product Code: CONM/30

List Price: $51.00

Individual Member Price: $40.80

**Electronic ISBN: 978-0-8218-7615-2
Product Code: CONM/30.E**

List Price: $51.00

Individual Member Price: $40.80

# Mathematical Applications of Category Theory

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*John W. Gray*

Mathematicians interested in understanding the directions of current research in set theory will not want to overlook this book, which contains the proceedings of the AMS Summer Research Conference on Axiomatic Set Theory, held in Boulder, Colorado, June 19–25, 1983. This was the first large meeting devoted exclusively to set theory since the legendary 1967 UCLA meeting, and a large majority of the most active research mathematicians in the field participated. All areas of set theory, including constructibility, forcing, combinatorics and descriptive set theory, were represented; many of the papers in the proceedings explore connections between areas. Readers should have a background of graduate-level set theory.

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#### Table of Contents

# Table of Contents

## Mathematical Applications of Category Theory

- Table of Contents vii8 free
- Introduction 110 free
- The Interaction Between Category Theory and Set Theory 514
- Synthetic Calculus of Variations 3039
- The Representation of Limits, Lax Limits and Homotopy Limits as Sections 6372
- Open Locales and Exponentiation 8493
- Eilenberg-Mac Lane Toposes and Cohomology 117126
- A Combinatorial Theory of Connections 132141
- Aspects of Higher Order Categorical Logic 145154
- A Stone-Type Representation Theory for First Order Logic 175184
- Topological Universes and Smooth Gelfand-Naimark Duality 244253
- Applications of the Dual Functor in Banach Spaces 277286