Relative Category Theory and Geometric Morphisms
A Logical Approach
Seiten
1992
Clarendon Press (Verlag)
978-0-19-853434-1 (ISBN)
Clarendon Press (Verlag)
978-0-19-853434-1 (ISBN)
Topos theory provides an important setting and language for much of mathematical logic and set theory. This book presents a convenient and natural solution to the treatment of geometric morphisms in this setting and shows how this may be applied to topics such as the relative Giraud theorem.
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.
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.
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.
| Erscheint lt. Verlag | 6.2.1992 |
|---|---|
| Reihe/Serie | Oxford Logic Guides ; 16 |
| Zusatzinfo | numerous line diagrams |
| Verlagsort | Oxford |
| Sprache | englisch |
| Maße | 164 x 238 mm |
| Gewicht | 566 g |
| Themenwelt | Mathematik / Informatik ► Mathematik ► Algebra |
| Mathematik / Informatik ► Mathematik ► Logik / Mengenlehre | |
| ISBN-10 | 0-19-853434-5 / 0198534345 |
| ISBN-13 | 978-0-19-853434-1 / 9780198534341 |
| Zustand | Neuware |
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