Ebook: Sheaves in Geometry and Logic: A First Introduction to Topos Theory

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.

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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.

---

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.
Content:
Front Matter....Pages i-xii
Prologue....Pages 1-9
Categorical Preliminaries....Pages 10-23
Categories of Functors....Pages 24-63
Sheaves of Sets....Pages 64-105
Grothendieck Topologies and Sheaves....Pages 106-160
First Properties of Elementary Topoi....Pages 161-217
Basic Constructions of Topoi....Pages 218-266
Topoi and Logic....Pages 267-346
Geometric Morphisms....Pages 347-420
Classifying Topoi....Pages 421-471
Localic Topoi....Pages 472-527
Geometric Logic and Classifying Topoi....Pages 528-573
Back Matter....Pages 574-630

---

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.
Content:
Front Matter....Pages i-xii
Prologue....Pages 1-9
Categorical Preliminaries....Pages 10-23
Categories of Functors....Pages 24-63
Sheaves of Sets....Pages 64-105
Grothendieck Topologies and Sheaves....Pages 106-160
First Properties of Elementary Topoi....Pages 161-217
Basic Constructions of Topoi....Pages 218-266
Topoi and Logic....Pages 267-346
Geometric Morphisms....Pages 347-420
Classifying Topoi....Pages 421-471
Localic Topoi....Pages 472-527
Geometric Logic and Classifying Topoi....Pages 528-573
Back Matter....Pages 574-630
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