Theories, Sites, Toposes: Relating and studying mathematical theories through topos-theoretic 'bridges'...

— —

Olivia Caramello (Mathematician, Mathematician, Università degli Studi dell'Insubria, Como, Italy)

Theories, Sites, Toposes

Relating and studying mathematical theories through topos-theoretic 'bridges'

Olivia Caramello (Mathematician, Mathematician, Università degli Studi dell'Insubria, Como, Italy)

$217

Hardback

Not in-store but you can order this
How long will it take?

Availability Information

We source books from suppliers in Australia and overseas. For books we don't currently have in stock, the time it takes to get them from our suppliers can vary widely - from a few days to a few months - so we check each book with each supplier to determine the expected time it will take to be supplied to us.

We then advise you accordingly. If the time taken to get any book is too long for you, you can let us know and we will cancel or adjust your order, and refund as required.

To find out the anticipated arrival time for specific items prior to ordering, please contact us by phone or email:

Phone +61 2 9264 3111, or 1800 4 BOOKS (1800 4 26657) if outside Sydney:
option 1 Abbey's Bookshop (Crime, History, Science, Kids & more) • info@abbeys.com.au
option 2 Language Book Centre (ESL & Foreign Languages) • language@abbeys.com.au
option 3 Galaxy Bookshop (Sci-fi, Fantasy, Romance, Graphic Novels) • sf@galaxybooks.com.au

QTY:

English

Oxford University Press
02 February 2017

Mathematics & Sciences; Philosophy of mathematics; Algebra; Geometry; Topology

"According to Grothendieck, the notion of topos is ""the bed or deep river where come to be married geometry and algebra, topology and arithmetic, mathematical logic and category theory, the world of the continuous and that of discontinuous or discrete structures"". It is what he had ""conceived of most broad to perceive with finesse, by the same language rich of geometric resonances, an ""essence"" which is common to situations most distant from each other, coming from one region or another of the vast universe of mathematical things"".

The aim of this book is to present a theory and a number of techniques which allow to give substance to Grothendieck's vision 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."

By: Olivia Caramello (Mathematician Mathematician Università degli Studi dell'Insubria Como Italy)
Imprint: Oxford University Press
Country of Publication: United Kingdom
Dimensions: Height: 236mm, Width: 164mm, Spine: 27mm
Weight: 1g
ISBN: 9780198758914
ISBN 10: 019875891X
Pages: 384
Publication Date: 02 February 2017
Audience: College/higher education , Professional and scholarly , A / AS level , Further / Higher Education
Format: Hardback
Publisher's Status: Active

Olivia Caramello is a mathematician working as Assistant Professor at the Universita degli Studi dell'Insubria in Como. Her research focuses on investigating the role of Grothendieck toposes as unifying spaces in Mathematics and Logic. Her main contribution has been the development of methods and techniques for transferring information between distinct mathematical theories by using toposes. After obtaining her Ph.D. in Mathematics at the University of Cambridge, she worked as a post-doctoral researcher at the Centro di Ricerca Matematica Ennio De Giorgi of the Scuola Normale Superiore (Pisa), Jesus College, Cambridge, the Max Planck Institute for Mathematics (Bonn), IHES, and as a Marie Curie Fellow at the Universite de Paris VII and the Universita degli Studi di Milano. She was awarded a L'Oreal-Unesco fellowship for Women in Science in 2014.

Reviews for Theories, Sites, Toposes: Relating and studying mathematical theories through topos-theoretic 'bridges'

The book is systematic, developing the subject from its very categorical beginning, assuming just the basic notions of category theory and a familiarity with first-order logic. This is a research monograph, but a dedicated reader would certainly profit from it. * Felipe Zaldivar, MAA Reviews *