Sketches of an Elephant: A Topos Theory Compendium (Oxford Logic Guides, 43 & 44) 1st Edition by Peter T. Johnstone (PDF)

Description

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. Now available in this two volume set, it contains all the important information both volumes provides. Considered to be a complete benefit for all researchers and academics in theoretical computer science, logicians and philosophers who study the foundations of mathematics, and those working in differential geometry and continuum physics.

User’s Reviews

Editorial Reviews: Review `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) About the Author Dr P.T. Johnstone Reader in the Foundations of Mathematics Dept of Pure Mathematics & Mathematical Statistics University of Cambridge Cambridge CB3 0BW

Reviews from Amazon users which were colected at the time this book was published on the website:

⭐good

⭐Very simply: if you want to know a very great deal about topos theory, buy this book. I mean, seriously, if you plan to make real work on topos theory a part of your life, then grit your teeth and come up with the money. If you do not want to know a very great deal about it, do not buy this book. You can use it at the library as a reference.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.

⭐It’s a comment on Colin MacLarty’s that it is rare for a top researcher to give so compendious a view of their field. I cannot add to Maclarty’s comment, who, himself is a top researcher, remarkable really. What I would like to say is that the desire for compendious-ness inheres in the British culture, a disciplined relentlessness to map out a domain. The field of Social Anthropology, is an instance of this, one that was initially a mapping out of ‘other cultures’ owes its development to a significant extent to that cultural bias. I know I will be tarred and feathered for saying this !! that: Shakespeare’s works constitute a complete mapping out (in the literary sphere) of the human condition for all ages. Even so Johnstone had a significantly easier job!

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