Categories, Allegories - 1st Edition - ISBN: 9780444703675, 9780080887012

Categories, Allegories, Volume 39

1st Edition

Authors: P.J. Freyd A. Scedrov
eBook ISBN: 9780080887012
Hardcover ISBN: 9780444703682
Imprint: North Holland
Published Date: 1st January 1990
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Table of Contents

Categories. Basic Definitions. Basic Examples and Constructions. Equivalence of Categories. Cartesian Categories. Regular Categories. Pre-Logoi. Logoi. Adjoint Functors, Grothendieck Topoi, and Exponential Categories. Topoi. Sconing.

Allegories. Basic Definitions. Distributive Allegories. Division Allegories. Power Allegories. Quotient Allegories. Appendices. Subject Index.


Description

General concepts and methods that occur throughout mathematics – and now also in theoretical computer science – are the subject of this book. It is a thorough introduction to Categories, emphasizing the geometric nature of the subject and explaining its connections to mathematical logic. The book should appeal to the inquisitive reader who has seen some basic topology and algebra and would like to learn and explore further.

The first part contains a detailed treatment of the fundamentals of Geometric Logic, which combines four central ideas: natural transformations, sheaves, adjoint functors, and topoi.

A special feature of the work is a general calculus of relations presented in the second part. This calculus offers another, often more amenable framework for concepts and methods discussed in part one. Some aspects of this approach find their origin in the relational calculi of Peirce and Schroeder from the last century, and in the 1940's in the work of Tarski and others on relational algebras. The representation theorems discussed are an original feature of this approach.


Details

Language:
English
Copyright:
© North Holland 1990
Published:
Imprint:
North Holland
eBook ISBN:
9780080887012
Hardcover ISBN:
9780444703682

Reviews

@from:H. Nishimura @qu:The book should be of interest to category theorists, mathematical logicians and theoretical computer scientists. @source:Zentralblatt fur Mathematik


About the Authors

P.J. Freyd Author

A. Scedrov Author

Affiliations and Expertise

University of Pennsylvania, Philadelphia, PA, USA