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Theories, sites, toposes : relating and studying mathematical theories through topos-theoretic 'bridges' / Olivia Caramello, Università degli Studi dell'Insubria - Como.

By: Caramello, Olivia [author.].
Material type: TextTextPublisher: Oxford : Oxford University Press, 2018Copyright date: ©2018Edition: First edition.Description: xii, 368 pages : UKP 65.00 illustrations ; 24 cm.Content type: text Media type: unmediated Carrier type: volumeISBN: 9780198758914 (hbk.); 019875891X.Subject(s): Toposes | ToposesDDC classification: 512.62 Summary: The aim of this book is to present a theory and a number of techniques which allow to give substance to Grothendieck's vision of the notion of topos. This has been accomplished by building on the notion of classifying topos educed by categorical logicians. Mathematical theories (formalized within first-order logic) give rise to geometric objects called sites; the passage from sites to their associated toposes embodies the passage from the logical presentation of theories to their mathematical content, i.e. from syntax to semantics. The essential ambiguity given by the fact that any topos is associated in general with an infinite number of theories or different sites allows to study the relations between different theories, and hence the theories themselves, by using toposes as 'bridges' between these different presentations. The expression or calculation of invariants of toposes in terms of the theories associated with them or their sites of definition generates a great number of results and notions varying according to the different types of presentation, giving rise to a veritable mathematical morphogenesis.-- Source other than Library of Congress.
List(s) this item appears in: 2018-09-07
Item type Current location Call number Status Date due Barcode Item holds
Book Chennai Mathematical Institute
General Stacks
512.62 CAR (Browse shelf) Available 10435
Total holds: 0

Includes bibliographical references (pages 359-362) and index.

The aim of this book is to present a theory and a number of techniques which allow to give substance to Grothendieck's vision of the notion of topos. This has been accomplished by building on the notion of classifying topos educed by categorical logicians. Mathematical theories (formalized within first-order logic) give rise to geometric objects called sites; the passage from sites to their associated toposes embodies the passage from the logical presentation of theories to their mathematical content, i.e. from syntax to semantics. The essential ambiguity given by the fact that any topos is associated in general with an infinite number of theories or different sites allows to study the relations between different theories, and hence the theories themselves, by using toposes as 'bridges' between these different presentations. The expression or calculation of invariants of toposes in terms of the theories associated with them or their sites of definition generates a great number of results and notions varying according to the different types of presentation, giving rise to a veritable mathematical morphogenesis.-- Source other than Library of Congress.