Topoi: The Categorial Analysis of Logic (Dover Books on Mathematics)

I have only read the first seventy pages of this book, but so far it is excellent. The character of the book can be likened to Kleene's "Introduction to Metamathematics" or "Mathematical Logic." The subject is well motivated by brief philosophical discussions, but the philosophy is not allowed to interrupt the flow of mathematical development. There are few exercises, but enough for the casual reader to check from time to time that he or she is understanding the material. The exposition itself is perfectly clear and concise, by my lights. Nothing important is skipped--one does not need to fill in the blanks in proofs--yet the book moves at a good pace. The focus of the book is on the development of Category theory in relation to its applications in logic. For this reason it is probably of more interest to a logician or a philosopher than to a computer scientist. Indeed, for the logician who is interested in Category theory this book cannot be missed. To put it bluntly, Goldblatt strikes me as a superior mind, even his brief remarks on set theory were enlightening. The book has been (to this point, at least) a very enjoyable read.

This book is an excellent introduction to category theory because it presents abstract category theory on the more concrete backdrop of logic. Category theory can get pretty abstract so this concrete connection to another area of Mathematics is necessary (unless you don't mind getting lost in abstraction). For best results, skim through the parts of the books that introduce category theory and move on to the main content of the book on logic. Then, refer back to the introductory parts as the main content demands. This way, there will be a clear purpose for each of the categorial concepts that you learn.

I bought this book because I was interested in applying topos theory to quantum mechanics but I had no knowledge of category theory. Looking for books on Amazon this seemed to me perfect because it not only explains topos theory but also offers an introduction to category theory. This introduction can be followed without problems for those who had no prior knowledge of category theory, in addition the book's style is clear and concise, motivating each concept introduced. Of course you can not read it like a novel, the reader must work each example and exercise to gain mastery over the issues.

This is an interesting addition to the field that was well ahead of the pack. Not as well written as Lawvere's later "Conceptual Mathematics" it covers more territory and becomes quite dense in its development of category theory which is now well established applied mathematics whose pure roots in sets is still evident.

very well written book starts with nontechnical chapters to technical ones. I would recommend this book as an advanced reading for students and researchers in the field of philosophy of mathematics and foundations of mathematics and logic.

Great Product!

Category theory, the alternative foundation for mathematics which privileges transformations over elements, has grown in importance and cachet in recent decades; however, for the average reader with intellectual interests the texts which treat of it have remained books with seven seals, containing seemingly-indecipherable "diagrams" not quite explaining the "abstract nonsense" (a term of approval among category theorists). Bricoleurs rejoice -- the second edition of Robert Goldblatt's *Topoi: The Categorial Analysis of Logic*, originally published by North-Holland in 1984, is available in an affordable Dover edition and is well worth your time. Like your usual North-Holland text, this is a book in *pure logic*: the "topos" (discovered by F. William Lawvere in the '60s) is the category which has the structure necessary to model quantificational logic, and Goldblatt's goal is to make the discoveries of Lawvere and others in this area available to people with a standard training in logical methods.Unlike your usual North-Holland book, *Topoi* contains well-paced introductions to all related topics, including basic category theory: I have never seen an introduction to category-theoretic "diagrams" which is as easy to follow, and I think those with previous logic training will agree. If you find Boolean algebras and "characteristic functions" natural, then Goldblatt's gradual introduction of categories that "parallel" logical structure will reinforce your understanding of logic and deepen your understanding of the related mathematics. The interesting fact about topos theory as a "model" for logic is that it does not privilege "classical" logic: the underlying logic of topoi is actually *intuitionistic*, and those with interests in intuitionism will be excited by what transpires in the book.Not only them, though: repeatedly throughout the later chapters of the book Goldblatt stresses the relevance of the results proved about intuitionism to *modal* logic, closely related through the "S4 translation" and the twinned Kripke semantics for intuitionism and modal logics. Philosophers tend to view "frame semantics" for modal logics as an unreasonably useful artifact delivered unto them by Providence, and thinking about its generalization using the idea of a "sheaf" will do them good. The book isn't absolutely everything it could be: "working mathematicians" will still need to look at Mac Lane or Steve Awodey's more recent *Category Theory* for the whole story, and computer scientists will find *Topoi* merely interesting (the connection between "cartesian closed categories" and effective computability, the fulcrum of category theory for CS, goes completely unremarked upon). However, for those looking for a "starting-point" with category theory this is definitely a good one.

If the title didn't scare you off, and you're reading this review, you'll likely enjoy this book. It's not in a category of it's own, but very cool.

This is a reprint of a book written in 1986, and it remains as a classic introduction to the complex and abstract mathematical subject of Toposes or topoi. The clarity of presentation contrasts with the absttract nature of the subject. As someone investigating the subject for the first time (at an advanced age) I am grateful to prof. Goldblatt for his evident seriousness of purpose and careful and clear presentation.If you want to learn about how sets might be replaced as foundations of mathematics, or understand more about intuitionistic logic, this is a help. If you are already at the postgraduate level in mathematics, you could benefit from the desire to be clear and write with a minimum orjargon or technical language.

Topoi theory as an evolution of category theory of mathematics is gaining more and more attention, even in theoretical physics enviroment.Goldblatt book is in my opinion the best introduction on this subject. Well and clearly written, by an outstanding logicist of our times.Deserves absolute attention by anyone interested in modern logic theories and (I think) in theoretical physics.Great book and (Dover edition...) great price!

After struggling through Mac's book I am finally beginning 'to get it'.

Je conseille vivement à ceux qui veulent entrer dans le monde des topos. Agréable à lire, très pédagogique, progressif et rigoureux.