Relative Category Theory and Geometric Morphisms: A Logical Approach

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Topos theory provides an important setting and language for much of mathematical logic and set theory. It is well known that a typed language can be given for a topos to be regarded as a category of sets. This enables a fruitful interplay between category theory and set theory. However, one stumbling block to a logical approach to topos theory has been the treatment of geometric morphisms. This book presents a convenient and natural solution to this problem by developing the notion of a frame relative to an ...

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Oxford, United Kingdom 1991 Hardcover First Edition Very Good. No Dust Jacket Used Plastic protected hardcover. Pages are clean and tight throughout. No dust jacket. T. ... *****PLEASE NOTE: This item is shipping from an authorized seller in Europe. In the event that a return is necessary, you will be able to return your item within the US. To learn more about our European sellers and policies see the BookQuest FAQ section***** Read more Show Less

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1992 Hard Cover Fine in Fine jacket 8vo-over 7?"-9?" tall. 263 pages. "The logical approach to topos theory, working with a language for a topos, has been hampered by ... difficulties in tackling proofs involving a geometric morphism (the most important notion of morphism between topoi). This is unfortunate, since a topos gives a radical notion of 'set' (or at least, of higher-order logic) and this approach deals with it as such." FINE HARDCOVER, ISSUED WITH A CLEAR PLASTIC DUST JACKET. Read more Show Less

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1992 Hardback 1st Edition Very Good/ glassine dustwrapper Pages. Nice clean bright tight book. *****PLEASE NOTE: This item is shipping from an authorized seller in Europe. In ... the event that a return is necessary, you will be able to return your item within the US. To learn more about our European sellers and policies see the BookQuest FAQ section***** Read more Show Less

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Overview

Topos theory provides an important setting and language for much of mathematical logic and set theory. It is well known that a typed language can be given for a topos to be regarded as a category of sets. This enables a fruitful interplay between category theory and set theory. However, one stumbling block to a logical approach to topos theory has been the treatment of geometric morphisms. This book presents a convenient and natural solution to this problem by developing the notion of a frame relative to an elementary topos. The authors show how this technique enables a logical approach to be taken to topics such as category theory relative to a topos and the relative Giraud theorem. The work is self-contained except that the authors presuppose a familiarity with basic category theory and topos theory. Logicians, set and category theorists, and computer scientist working in the field will find this work essential reading.

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Product Details

  • ISBN-13: 9780198534341
  • Publisher: Oxford University Press, USA
  • Publication date: 3/5/1992
  • Series: Oxford Logic Guides Series , #16
  • Pages: 280
  • Product dimensions: 6.38 (w) x 9.50 (h) x 0.83 (d)

Table of Contents

1. Introduction

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