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Relative Category Theory and Geometric Morphisms: A Logical Approach - Couverture rigide

Chapman, Jonathan; Rowbottom, Frederick

 
9780198534341: Relative Category Theory and Geometric Morphisms: A Logical Approach
Couverture rigide
ISBN 10 : 0198534345 ISBN 13 : 9780198534341
Editeur : Clarendon Press, 1992

Synopsis

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.

Les informations fournies dans la section « Synopsis » peuvent faire référence à une autre édition de ce titre.

Présentation de l'éditeur

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.

Revue de presse

'The present book represents what must surely be an extreme point in the spectrum of possible approaches: the one which makes the greatest possible use of formal languages. The material, throughtout the books, is of a highly technical nature ... By providing a language adequate to handle indexed categories over a topos (and much more besides), the authors have done much to "demystify" indexed category theory and make it accessible to those for whom the sight of a 2-categorical diagram is liable to induce instant incomprehension. All such people ... should make the effort to master the technicalities in this book, if they wish to get closer to an understanding of what really goes on in the 2-category of toposes.' P.T. Johnstone, Zentralblatter, 1993

Les informations fournies dans la section « A propos du livre » peuvent faire référence à une autre édition de ce titre.

Éditeur
Clarendon Press
Date d'édition
1992
Langue
anglais
ISBN 10 
0198534345
ISBN 13 
9780198534341
Reliure
Relié
Numéro d'édition
1
Nombre de pages
276
Coordonnées du fabricant
non disponible
Personne responsable
Ufficio Anagrafiche Messaggerie
ufficio.anagrafiche@meli.it

Via Verdi, 8
Assago Milano
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Italie