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

Olivia Caramello

Abstract

This book is devoted to a general study of geometric theories from a topos-theoretic perspective. After recalling the necessary topos-theoretic preliminaries, it presents the main methodology it uses to extract ‘concrete’ information on theories from properties of their classifying toposes—the ‘bridge’ technique. As a first implementation of this methodology, a duality is established between the subtoposes of the classifying topos of a geometric theory and the geometric theory extensions (also called ‘quotients’) of the theory. Many concepts of elementary topos theory which apply to the lattic ... More

Keywords: geometric theory, classifying topos, subtopos, duality, quotient, bridge, flat functor, presheaf topos, model, expansion of theory

Bibliographic Information

Print publication date: 2017 Print ISBN-13: 9780198758914
Published to Oxford Scholarship Online: March 2018 DOI:10.1093/oso/9780198758914.001.0001

Authors

Affiliations are at time of print publication.

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