Relative category theory and geometric morphisms : a logical approach
Author(s)
Bibliographic Information
Relative category theory and geometric morphisms : a logical approach
（Oxford logic guides, 16）
Clarendon Press , Oxford University Press, 1992
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Note
Includes bibliographical references (p. [255]-257) and index
Description and Table of Contents
Description
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 which allows 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 essentially self-contained except that the authors presuppose a familiarity with basic category theory and topos theory.
Table of Contents
- Introduction
- Local set theories
- Partial function theory `L'
- Equationals
- Categories in a topos
- Topoi in a topos
- A representation theorem for geometric morphisms
- Local set theories in S
- The theory of a topos in S
- Topologies and sheaves
- The relative Giraud theorem
- Appendices.
by "Nielsen BookData"