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.

zlib/no-category/Mac Lane, Saunders; Moerdijk, Ieke/[Universitext] Sheaves in Geometry and Logic ||_55656186.pdf

[Universitext] Sheaves in Geometry and Logic ||

Saunders MacLane, Ieke Moerdijk, Saunders Mac Lane

Mac Lane, Saunders; Moerdijk, Ieke

Springer London, Limited

Springer Nature (Textbooks & Major Reference Works), New York, NY, 2012

United States, United States of America

Universitext, New York, NY, 1994

Universitext, New York, NY, 1992

sm23268855

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.

2015-07-15