Sheaves in Geometry and Logic

1. Front Matter

   Pages i-xii

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2. Prologue

   • Saunders Mac Lane, Ieke Moerdijk

   Pages 1-9

3. Categorical Preliminaries

   • Saunders Mac Lane, Ieke Moerdijk

   Pages 10-23

4. Categories of Functors

   • Saunders Mac Lane, Ieke Moerdijk

   Pages 24-63

5. Sheaves of Sets

   • Saunders Mac Lane, Ieke Moerdijk

   Pages 64-105

6. Grothendieck Topologies and Sheaves

   • Saunders Mac Lane, Ieke Moerdijk

   Pages 106-160

7. First Properties of Elementary Topoi

   • Saunders Mac Lane, Ieke Moerdijk

   Pages 161-217

8. Basic Constructions of Topoi

   • Saunders Mac Lane, Ieke Moerdijk

   Pages 218-266

9. Topoi and Logic

   • Saunders Mac Lane, Ieke Moerdijk

   Pages 267-346

10. Geometric Morphisms

    • Saunders Mac Lane, Ieke Moerdijk

    Pages 347-420

11. Classifying Topoi

    • Saunders Mac Lane, Ieke Moerdijk

    Pages 421-471

12. Localic Topoi

    • Saunders Mac Lane, Ieke Moerdijk

    Pages 472-527

13. Geometric Logic and Classifying Topoi

    • Saunders Mac Lane, Ieke Moerdijk

    Pages 528-573

14. Erratum

    • Saunders Mac Lane, Ieke Moerdijk

    Pages E1-E1

15. Back Matter

    Pages 574-630

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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.

• Algebraic structure
• Boolean algebra
• Division
• Heyting algebra
• forcing
• set
• set theory

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)

• Department of Mathematics, University of Chicago, Chicago, USA

  Saunders Mac Lane

• Mathematical Institute, University of Utrecht, Utrecht, The Netherlands

  Ieke Moerdijk

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