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Sheaves in Geometry and Logic A First Introduction to Topos Theory
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Located in: Lansdale, PA, United States
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eBay item number:357181741561
Item specifics
- Condition
- Brand New: A new, unread, unused book in perfect condition with no missing or damaged pages. See all condition definitionsopens in a new window or tab
- ISBN
- 9780387977102
About this product
Product Identifiers
Publisher
Springer New York
ISBN-10
0387977104
ISBN-13
9780387977102
eBay Product ID (ePID)
117839
Product Key Features
Number of Pages
Xii, 630 Pages
Publication Name
Sheaves in Geometry and Logic : a First Introduction to Topos Theory
Language
English
Subject
Group Theory, Algebra / Abstract, Geometry / General, Algebra / General, Logic
Publication Year
1992
Type
Textbook
Subject Area
Mathematics
Series
Universitext Ser.
Format
Trade Paperback
Dimensions
Item Weight
70.2 Oz
Item Length
9.3 in
Item Width
6.1 in
Additional Product Features
Intended Audience
Scholarly & Professional
LCCN
91-033709
Reviews
From the reviews: "A beautifully written book, a long and well motivated book packed with well chosen clearly explained examples. … authors have a rare gift for conveying an insider's view of the subject from the start. This book is written in the best Mac Lane style, very clear and very well organized. … it gives very explicit descriptions of many advanced topics--you can learn a great deal from this book that, before it was published, you could only learn by knowing researchers in the field." (Wordtrade, 2008), From the reviews: "A beautifully written book, a long and well motivated book packed with well chosen clearly explained examples. ... authors have a rare gift for conveying an insider's view of the subject from the start. This book is written in the best Mac Lane style, very clear and very well organized. ... it gives very explicit descriptions of many advanced topics--you can learn a great deal from this book that, before it was published, you could only learn by knowing researchers in the field." (Wordtrade, 2008), From the reviews:"A beautifully written book, a long and well motivated book packed with well chosen clearly explained examples. … authors have a rare gift for conveying an insider's view of the subject from the start. This book is written in the best Mac Lane style, very clear and very well organized. … it gives very explicit descriptions of many advanced topics--you can learn a great deal from this book that, before it was published, you could only learn by knowing researchers in the field." (Wordtrade, 2008)
Number of Volumes
1 vol.
Illustrated
Yes
Table Of Content
Prologue.- Categorial Preliminaries.- I. Categories of Functors.- 1. The Categories at Issue.- 2. Pullbacks.- 3. Characteristic Functions of Subobjects.- 4. Typical Subobject Classifiers.- 5. Colimits.- 6. Exponentials.- 7. Propositional Calculus.- 8. Heyting Algebras.- 9. Quantifiers as Adjoints.- Exercises.- II. Sheaves of Sets.- 1. Sheaves.- 2. Sieves and Sheaves.- 3. Sheaves and Manifolds.- 4. Bundles.- 5. Sheaves and Cross-Sections.- 6. Sheaves as Étale Spaces.- 7. Sheaves with Algebraic Structure.- 8. Sheaves are Typical.- 9. Inverse Image Sheaf.- Exercises.- III. Grothendieck Topologies and Sheaves.- 1. Generalized Neighborhoods.- 2. Grothendieck Topologies.- 3. The Zariski Site.- 4. Sheaves on a Site.- 5. The Associated Sheaf Functor.- 6. First Properties of the Category of Sheaves.- 7. Subobject Classifiers for Sites.- 8. Subsheaves.- 9. Continuous Group Actions.- Exercises.- IV. First Properties of Elementary Topoi.- 1. Definition of a Topos.- 2. The Construction of Exponentials.- 3. Direct Image.- 4. Monads and Beck's Theorem.- 5. The Construction of Colimits.- 6. Factorization and Images.- 7. The Slice Category as a Topos.- 8. Lattice and Heyting Algebra Objects in a Topos.- 9. The Beck-Chevalley Condition.- 10. Injective Objects.- Exercises.- V. Basic Constructions of Topoi.- 1. Lawvere-Tierney Topologies.- 2. Sheaves.- 3. The Associated Sheaf Functor.- 4. Lawvere-Tierney Subsumes Grothendieck.- 5. Internal Versus External.- 6. Group Actions.- 7. Category Actions.- 8. The Topos of Coalgebras.- 9. The Filter-Quotient Construction.- Exercises.- VI. Topoi and Logic.- 1. The Topos of Sets.- 2. The Cohen Topos.- 3. The Preservation of Cardinal Inequalities.- 4. The Axiom of Choice.- 5. The Mitchell-Bénabou Language.- 6. Kripke-Joyal Semantics.- 7. Sheaf Semantics.- 8. Real Numbers in a Topos.- 9. Brouwer's Theorem: All Functions are Continuous.- 10. Topos-Theoretic and Set-Theoretic Foundations.- Exercises.- VII. Geometric Morphisms.- 1. Geometric Morphismsand Basic Examples.- 2. Tensor Products.- 3. Group Actions.- 4. Embeddings and Surjections.- 5. Points.- 6. Filtering Functors.- 7. Morphisms into Grothendieck Topoi.- 8. Filtering Functors into a Topos.- 9. Geometric Morphisms as Filtering Functors.- 10. Morphisms Between Sites.- Exercises.- VIII. Classifying Topoi.- 1. Classifying Spaces in Topology.- 2. Torsors.- 3. Classifying Topoi.- 4. The Object Classifier.- 5. The Classifying Topos for Rings.- 6. The Zariski Topos Classifies Local Rings.- 7. Simplicial Sets.- 8. Simplicial Sets Classify Linear Orders.- Exercises.- IX. Localic Topoi.- 1. Locales.- 2. Points and Sober Spaces.- 3. Spaces from Locales.- 4. Embeddings and Surjections of Locales.- 5. Localic Topoi.- 6. Open Geometric Morphisms.- 7. Open Maps of Locales.- 8. Open Maps and Sites.- 9. The Diaconescu Cover and Barr's Theorem.- 10. The Stone Space of a Complete Boolean Algebra.- 11. Deligne's Theorem.- Exercises.- X. Geometric Logic and Classifying Topoi.- 1. First-OrderTheories.- 2. Models in Topoi.- 3. Geometric Theories.- 4. Categories of Definable Objects.- 5. Syntactic Sites.- 6. The Classifying Topos of a Geometric Theory.- 7. Universal Models.- Exercises.- Appendix: Sites for Topoi.- Epilogue.- Index of Notation.
Synopsis
This text presents topos theory as it has developed from the study of sheaves. Beginning with several illustrative examples, the book explains the underlying ideas of topology and sheaf theory as well as the general theory of elementary toposes and geometric morphisms and their relation to logic., This text presents topos theory as it has developed from the study of sheaves. Sheaves arose in geometry as coefficients for cohomology and as descriptions of the functions appropriate to various kinds of manifolds (algebraic, analytic, etc.). Sheaves also appear in logic as carriers for models of set theory as well as for the semantics of other types of logic. Grothendieck introduced a topos as a category of sheaves for algebraic geometry. Subsequently, Lawvere and Tierney obtained elementary axioms for such (more general) categories., We dedicate this book to the memory of J. Frank Adams. His clear insights have inspired many mathematicians, including both of us. In January 1989, when the first draft of our book had been completed, we heard the sad news of his untimely death. This has cast a shadow on our subsequent work. Our views of topos theory, as presented here, have been shaped by continued study, by conferences, and by many personal contacts with friends and colleagues-including especially O. Bruno, P. Freyd, J.M.E. Hyland, P.T. Johnstone, A. Joyal, A. Kock, F.W. Lawvere, G.E. Reyes, R Solovay, R Swan, RW. Thomason, M. Tierney, and G.C. Wraith. Our presentation combines ideas and results from these people and from many others, but we have not endeavored to specify the various original sources. Moreover, a number of people have assisted in our work by pro viding helpful comments on portions of the manuscript. In this respect, we extend our hearty thanks in particular to P. Corazza, K. Edwards, J. Greenlees, G. Janelidze, G. Lewis, and S. Schanuel., We dedicate this book to the memory of J. Frank Adams. His clear insights have inspired many mathematicians, including both of us. In January 1989, when the first draft of our book had been completed, we heard the sad news of his untimely death. This has cast a shadow on our subsequent work. Our views of topos theory, as presented here, have been shaped by continued study, by conferences, and by many personal contacts with friends and colleagues-including especially O. Bruno, P. Freyd, J.M.E. Hyland, P.T. Johnstone, A. Joyal, A. Kock, F.W. Lawvere, G.E. Reyes, R Solovay, R Swan, RW. Thomason, M. Tierney, and G.C. Wraith. Our presentation combines ideas and results from these people and from many others, but we have not endeavored to specify the various original sources. Moreover, a number of people have assisted in our work by pro- viding helpful comments on portions of the manuscript. In this respect, we extend our hearty thanks in particular to P. Corazza, K. Edwards, J. Greenlees, G. Janelidze, G. Lewis, and S. Schanuel.
LC Classification Number
QA440-699
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- 7***7 (34)- Feedback left by buyer.Past 6 monthsVerified purchaseFast shipping and a secure packaging. Thank you.Mozart: Die Zauberflote (The Magic Flute) Vocal Score (#357036074979)
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