- Tapa dura: 1288 páginas
- Editor: Clarendon Press (12 de septiembre de 2002)
- Colección: Oxford Logic Guides
- Idioma: Inglés
- ISBN-10: 019852496X
- ISBN-13: 978-0198524960
- Valoración media de los clientes: Sé el primero en opinar sobre este producto
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Sketches of an Elephant: A Topos Theory Compendium: 2 Volume Set (Oxford Logic Guides) (Inglés) Tapa dura – 12 sep 2002
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Descripción del producto
Specialists of topos theory were expecting this Elephant since many years. It is extremely good news that the first two volumes already appeared, without waiting for the completion of the third one. (Bulletin of the Belgian Mathematical Society)
This compendium contains material that was previously available only in specialist journals. This is likely to become the standard reference work for all those interested in the subject. (? News (The Newsletter for Philosophical Logic and Its Applications))
Reseña del editor
Topos Theory is a subject that stands at the junction of geometry, mathematical logic and theoretical computer science, and it derives much of its power from the interplay of ideas drawn from these different areas. Because of this, an account of topos theory which approaches the subject from one particular direction can only hope to give a partial picture; the aim of this compendium is to present as comprehensive an account as possible of all the main approaches and thereby to demonstrate the overall unity of the subject. The material is organised in such a way that readers interested in following a particular line of approach may do so by starting at an appropriate point in the text.Ver Descripción del producto
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If you merely want a professional understanding of what topos theory is, then read Johnstone's earlier TOPOS THEORY. That far shorter book gives a better overview. My Amazon review of it discusses others on the subject. Most are more accessible than Johnstone's books and go more into particular aspects of the theory.
This book is a reference on all the methods, and the latest results, in topos theory. If you want the definition of "split opfibration", it is here, along with some 80 pages of background, examples, and motivation. Johnstone does an heroic job of unifying the terminology and organizing the theorems.
More than that, Johnstone has written down an expert, encyclopedic view of the subject today. It is rare for a top mathematical researcher to give so deep an account of their field. It is rare for anyone to even work out such an explicit, coherent, extensive account of the whole. Not everyone will agree with his view. Some would like to see much less of such logical topics as "allegories", others would like to see the logic more formalized from the start. But Johnstone builds a case for his choices: partly implicit in his success at explaining things this way, and partly by explicit reasons.
If you want to know that much about the subject then you want to immerse yourself in this book.