[FOM] Fwd: Book on toposes

[Martin Davis]

---------- Forwarded message ----------
From: Olivia Caramello <olivia at oliviacaramello.com>
Date: Sun, Dec 24, 2017 at 9:46 AM
Subject: Book on toposes

I am pleased to announce the publication of my book “Theories, Sites,
Toposes: Relating and studying mathematical theories through
topos-theoretic ‘bridges’” (384 pages) by Oxford University Press:

https://global.oup.com/academic/product/theories-
sites-toposes-9780198758914?cc=gb&lang=en#

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 theory of classifying toposes – which
geometrically embodies the mathematical content of first-order (geometric)
theories - is first recalled, allowing the formulation of general ‘bridge’
principles: study theories through the computation of invariants of their
associated toposes in terms of different presentations of these toposes. As
any Grothendieck topos has infinitely many presentations, the expression of
its invariants in terms of them gives rise to a veritable mathematical
morphogenesis. These methods, which are susceptible to unify notions and
results across distinct mathematical areas, are applied in particular to
the study of geometric theories and their extensions through suitable
topos-theoretic invariants. The book concludes with a selection of
applications of the theoretical results obtained in the previous parts to
very different concrete mathematical theories.

All the best,

Olivia Caramello
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