Relative Category Theory and Geometric Morphisms

A Logical Approach
Erscheinungsjahr 1992
ISBN: 978-0-19-853434-1
Verlag: Oxford University Press

Buch, Englisch, 276 Seiten, Print PDF, Format (B × H): 164 mm x 238 mm, Gewicht: 566 g

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.

Autoren/Hrsg.

Chapman, Jonathan

Rowbottom, Frederick

Fachgebiete

• Mathematik | Informatik Mathematik Mathematik Allgemein Mathematische Logik
• Mathematik | Informatik Mathematik Algebra

Inhaltsverzeichnis

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.