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Sheaves in Geometry and Logic: A First Introduction to Topos Theory (Universitext) Paperback – June 1, 1992

ISBN-13: 978-3540977100 ISBN-10: 3540977104

 
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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)

--This text refers to an alternate Paperback edition.
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Product Details

  • Series: Universitext
  • Paperback: 639 pages
  • Publisher: Springer-Verlag Berlin and Heidelberg GmbH & Co. K (June 1992)
  • Language: English
  • ISBN-10: 3540977104
  • ISBN-13: 978-3540977100
  • Product Dimensions: 9.2 x 5.9 x 1.3 inches
  • Shipping Weight: 2 pounds
  • Average Customer Review: 5.0 out of 5 stars  See all reviews (5 customer reviews)
  • Amazon Best Sellers Rank: #11,107,394 in Books (See Top 100 in Books)

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Also a great book in topoi theory, from the basics up to the Cohen topos.
luis
Several examples of categories with the Grothendieck topologies are discussed, one of these being a complete Heyting algebra.
Dr. Lee D. Carlson
This book is written in the best Mac Lane style, very clear and very well organized.
Colin McLarty

Most Helpful Customer Reviews

30 of 33 people found the following review helpful By Dr. Lee D. Carlson HALL OF FAMEVINE VOICE on May 1, 2005
Format: Paperback Verified Purchase
Topos theory now has applications in fields such as music theory, quantum gravity, artificial intelligence, and computer science. It has been viewed by some as being excessively abstract and difficult to learn, and this is certainly true if one attempts to learn it from the research literature. The use of this book to learn topos theory certainly puts this view to rest, as the authors have given the readers an introduction to topos theory that is crystal clear and nicely motivated from an historical point of view. Indeed the prologue to the book gives the reader a deep appreciation of the origins of the subject, and could even serve as an introduction to a class on algebraic geometry.

An understanding of sheaf theory and category theory will definitely help when attempting to learn topos theory, but the book could be read without such a background. Readers who want to read the chapters on logic and geometric morphisms will need a background in mathematical logic and set theory in order to appreciate them. Topos theory has recently been used in research in quantum gravity. A reader interested in understanding how topos theory is used in this research should concentrate on the chapter on properties of elementary topoi, the one on basic categories of topoi, and the chapter on localic topoi.

The authors introduce topos theory as a tool for unifying topology with algebraic geometry and as one for unifying logic and set theory. The latter application is interesting, especially for readers (such as this reviewer), who approach the book from the standpoint of the former. Indeed, the authors discuss a fascinating use of topos theory by Paul Cohen in his proof of the independence of the Continuum Hypothesis in Zermelo-Fraenkel set theory.
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30 of 34 people found the following review helpful By Colin McLarty on March 27, 2000
Format: Paperback
This book is written in the best Mac Lane style, very clear and very well organized. It also benefits from Moerdijk's extensive work organizing the theory of Grothendieck toposes by elementary means. The reader should have basic graduate knowledge of algebra and topology. The book is long because 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.
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11 of 11 people found the following review helpful By Gary L. Herstein on April 9, 2013
Format: Kindle Edition Verified Purchase
Several folks have already commented on how this volume provides an excellent formal introduction to category theory and topoi. I have nothing to add to those excellent reviews and encourage others to read them. What I wish to do here is comment on a somewhat tangential subject of my own interest, and that is the philosophy of logic.

This book makes clear the very significant connections between logic, what I would call "general spatial reasoning," and category theory. For anyone interested in the underlying core and structure of formal reasoning beyond the questionable dogmas of Russell-Frege proof-theoretic approaches, this book is an absolute must have. The proof-theoretic methods that have swamped the thinking about logic in most philosophical circles has seriously undermined our understanding of the relevant issues by blinding scholars to the genuine wealth of ideas that exists within mathematics. I would argue that this book, in conjunction with such works as Corry's "Rise of Modern Algebra" (see inserted link) is a fundamental step away from the shackles of the Russell-Frege vision of formal logic that dominates so much thought in the philosophy of logic. (Corry's work places algebraic thinking within an historical context that the mere formal study of the subject tramples right over. Such historical context is an essential element in the philosophical -- as opposed to purely formal -- study of such topics.)

The materials in _Sheaves_ are presented in an accessible way for the non-mathematician, *provided* that person still has a reasonably solid background in some such topic(s) as formal logic, model theory, abstract algebra, etc.
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2 of 2 people found the following review helpful By Linas Vepstas on June 16, 2013
Format: Paperback Verified Purchase
Clear, to the point, readable. Not too hard, not too easy. Assumes some general familiarity with categories, but not too much. Everything is developed at a hearty clip: plenty of curt examples; avoids tedium by getting to the point. Ideal if you're mature and interested in mathematics in general, and have the time to set your own pace. Might be a bit challenging for inexperienced grad students on a forced march -- or not. Doable.
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2 of 2 people found the following review helpful By luis on January 5, 2012
Format: Paperback Verified Purchase
This is a really good book to learn sheaves, it has the "tree generations" of sheaves; with topological spaces, with Grothendieck topologies, and with Lawvere-Tirney topologies. Also a great book in topoi theory, from the basics up to the Cohen topos.
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