Sheaves in geometry and logic : a first introduction to topos theory
著者
書誌事項
Sheaves in geometry and logic : a first introduction to topos theory
（Universitext）
Springer, 1994, c1992
2nd corr. printing
- : us
- : gw
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注記
Bibliography: p. 605-614
Incudes indexes
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内容説明・目次
- 巻冊次
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: us ISBN 9780387977102
内容説明
Sheaves arose in geometry as coefficients for cohomology and as descriptions of the functions appropriate to various kinds of manifolds. Sheaves also appear in logic as carriers for models of set theory. This text presents topos theory as it has developed from the study of sheaves. Beginning with several examples, it 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.
目次
- Preface
- Prologue
- Categorical Preliminaries
- 1. Categories of Functors
- 2. Sheaves of Sets
- 3. Grothendieck Topologies and Sheaves
- 4. First Properties of Elementary Topoi
- 5. Basic Constructions of Topoi
- 6. Topoi and Logic
- 7. Geometric Morphisms
- 8. Classifying Topoi
- 9. Localic Topoi
- 10. Geometric Logic and Classifying Topoi
- Appendix: Sites for Topoi
- Epilogue
- Bibliography
- Index of Notations
- Index
- 巻冊次
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: gw ISBN 9783540977100
内容説明
This introduction to the theory of toposes (developed by Grothendieck and followed up by Lawvere and Tierney) begins with illustrative examples and goes on to explain 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.
目次
Contents: Categories of Functors.- Sheaves of Sets.- Grothendieck Topologies and Sheaves.- First Properties of Elementary Topoi.- Basic Constructions of Topoi.- Topoi and Logic.- Geometric Morphisms.- Classifying Topoi.- Localic Topoi.- Geometric Logic and Classifying Topoi.- Appendix: Sites for Topoi.
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