Theories, Sites, Toposes

This book introduces a set of methods and techniques for studying mathematical theories and relating them to each other through the use of Grothendieck toposes.

Zusatztext 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. Informationen zum Autor Olivia Caramello is a mathematician working as Assistant Professor at the Università 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 ofCambridge, 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 Université de Paris VII and the Università degli Studidi Milano. She was awarded a L'Oréal-Unesco fellowship for Women in Science in 2014. Klappentext This book introduces a set of methods and techniques for studying mathematical theories and relating them to each other through the use of Grothendieck toposes. Zusammenfassung This book introduces a set of methods and techniques for studying mathematical theories and relating them to each other through the use of Grothendieck toposes.

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.

Autorentext
Olivia Caramello is a mathematician working as Assistant Professor at the Università 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 Université de Paris VII and the Università degli Studi di Milano. She was awarded a L'Oréal-Unesco fellowship for Women in Science in 2014.

Inhalt
1: Topos-theoretic background
2: Classifying toposes and the 'bridge' technique
3: A duality theorem
4: Lattices of theories
5: Flat functors and classifying toposes
6: Theories of presheaf type: general criteria
7: Expansions and faithful interpretations
8: Quotients of a theory of presheaf type
9: Examples of theories of presheaf type
10: Some applications

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