Topos theory (eBook, 2014) [WorldCat.org]
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Topos theory

Author: P T Johnstone
Publisher: Mineola, New York : Dover Publications, Incorporated, 2014.
Series: Dover books on mathematics.
Edition/Format:   eBook : Document : English : Dover editionView all editions and formats
Summary:
One of the best books on a relatively new branch of mathematics, this text is the work of a leading authority in the field of topos theory. Suitable for advanced undergraduates and graduate students of mathematics, the treatment focuses on how topos theory integrates geometric and logical ideas into the foundations of mathematics and theoretical computer science.After a brief overview, the approach begins with  Read more...
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Genre/Form: Electronic books
Material Type: Document, Internet resource
Document Type: Internet Resource, Computer File
All Authors / Contributors: P T Johnstone
ISBN: 1306329000 9781306329002 9780486783093 048678309X
OCLC Number: 1162600793
Language Note: English.
Notes: "This Dover edition, first published by Dover Publications, Inc., in 2014, is an unabridged republication of the work originally published by Academic Press, Inc., New York, in 1977--Title page verso."
Description: 1 online resource (740 p.).
Contents: Cover; Title Page; Copyright Page; Preface; Contents; Introduction; Notes for the Reader; Chapter 0: Preliminaries; 0.1 Category Theory; 0.2 Sheaf Theory; 0.3 Grothendieck Topologies; 0.4 Giraud's Theorem; Exercises 0; Chapter 1: Elementary Toposes; 1.1 Definition and Examples; 1.2 Equivalence Relations and Partial Maps; 1.3 The Category op; 1.4 Pullback Functors; 1.5 Image Factorizations; Exercises 1; Chapter 2: Internal Category Theory; 2.1 Internal Categories and Diagrams; 2.2 Internal Limits and Colimits; 2.3 Diagrams in a Topos; 2.4 Internal Profunctors; 2.5 Filtered Categories Exercises 2Chapter 3: Topologies and Sheaves; 3.1 Topologies; 3.2 Sheaves; 3.3 The Associated Sheaf Functor; 3.4 sh j() as a Category of Fractions; 3.5 Examples of Topologies; Exercises 3; Chapter 4: Geometric Morphisms; 4.1 The Factorization Theorem; 4.2 The Glueing Construction; 4.3 Diaconescu's Theorem; 4.4 Bounded Morphisms; Exercises 4; Chapter 5: Logical Aspects of Topos Theory; 5.1 Boolean Toposes; 5.2 The Axiom of Choice; 5.3 The Axiom (SG); 5.4 The Mitchell-Bénabou Language; Exercises 5; Chapter 6: Natural Number Objects; 6.1 Definition and Basic Properties; 6.2 Finite Cardinals 6.3 The Object Classifier6.4 Algebraic Theories; 6.5 Geometric Theories; 6.6 Real Number Objects; Exercises 6; Chapter 7: Theorems of Deligne and Barr; 7.1 Points; 7.2 Spatial Toposes; 7.3 Coherent Toposes; 7.4 Deligne's Theorem; 7.5 Barr's Theorem; Exercises 7; Chapter 8: Cohomology; 8.1 Basic Definitions; 8.2 Cech Cohomology; 8.3 Torsors; 8.4 Profinite Fundamental Groups; Exercises 8; Chapter 9: Topos Theory and Set Theory; 9.1 Kuratowski-Finiteness; 9.2 Transitive Objects; 9.3 The Equiconsistency Theorem; 9.4 The Filterpower Construction; 9.5 Independence of the Continuum Hypothesis Exercises 9Appendix: Locally Internal Categories; Bibliography; Index of Definitions; Index of Notation; Index of Names
Series Title: Dover books on mathematics.
Responsibility: P.T. Johnstone, Dept. of Pure Mathematics and Mathematical Statistics, University of Cambridge, Cambridge, England.

Abstract:

One of the best books on a relatively new branch of mathematics, this text is the work of a leading authority in the field of topos theory. Suitable for advanced undergraduates and graduate students of mathematics, the treatment focuses on how topos theory integrates geometric and logical ideas into the foundations of mathematics and theoretical computer science.After a brief overview, the approach begins with elementary toposes and advances to internal category theory, topologies and sheaves, geometric morphisms, and logical aspects of topos theory. Additional topics include natural number ob.

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