Sheaves in Geometry and Logic
A First Introduction to Topos Theory
(Sprache: Englisch)
This book is an introduction to the theory of toposes, as first developed by Grothendieck and later developed by Lawvere and Tierney. Beginning with several illustrative examples, the book explains the underlying ideas of topology and sheaf theory as well...
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This book is an introduction to the theory of toposes, as first developed by Grothendieck and later developed by Lawvere and Tierney. 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 is the first text to address all of these various aspects of topos theory at the graduate student level.
Klappentext zu „Sheaves in Geometry and Logic “
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.
Inhaltsverzeichnis zu „Sheaves in Geometry and Logic “
- 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.
Bibliographische Angaben
- Autoren: Saunders MacLane , Ieke Moerdijk
- 1992, 1992, XII, 630 Seiten, Maße: 15,5 x 23,5 cm, Kartoniert (TB), Englisch
- Verlag: Springer, Berlin
- ISBN-10: 0387977104
- ISBN-13: 9780387977102
- Erscheinungsdatum: 27.10.1994
Sprache:
Englisch
Rezension zu „Sheaves in Geometry and Logic “
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Pressezitat
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)
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