Keywords
Team
Conception pour les transitions et transformations industrielles
Biography
Olivia Caramello is a researcher whose work lies at the intersection of topos theory, categorical logic, and the foundations of mathematics. Her research focuses primarily on developing unifying methods in mathematics by using Grothendieck topos as “bridges” to transfer concepts, results, and structures between distinct mathematical theories. She has helped formalize this approach, notably through the theory of “topos-theoretical bridges,” which provides a systematic framework for connecting diverse fields such as algebra, geometry, and model theory. Her work also includes advances in geometric logic, categorical dualities, and generalizations of Galois formalisms, with applications in MV-algebra theory, universal algebra, and motivic cohomology. His expertise also extends to the characterization of geometric theories classified by specific topos, as well as the study of the logical properties of topos, such as the validity of De Morgan’s law or the law of the excluded middle.
Publication(s)
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2023
THE OVER-TOPOS AT A MODEL
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2022
The Unification of Mathematics via Topos Theory DOI : 10.1007/978-3-030-94452-0_30
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2022
Grothendieck Toposes as Unifying ‘Bridges’: A Mathematical Morphogenesis DOI : 10.1007/978-3-030-84706-7_9
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2021
On the dependent product in toposes DOI : 10.1002/malq.202000069
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2021
General affine adjunctions, Nullstellensätze, and dualities DOI : 10.1016/j.jpaa.2020.106470
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2019
Some aspects of topological Galois theory DOI : 10.1016/j.geomphys.2019.04.004
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2018
Syntactic categories for Nori motives DOI : 10.1007/s00029-018-0425-z
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2018
Theories, sites, toposes: Relating and studying mathematical theories through topos-theoretic 'bridges' DOI : 10.1093/oso/9780198758914.001.0001
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2017
On the geometric theory of local MV-algebras DOI : 10.1016/j.jalgebra.2017.01.005
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2017
Cyclic Theories DOI : 10.1007/s10485-015-9414-y
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2016
LATTICE-ORDERED ABELIAN GROUPS and PERFECT MV-ALGEBRAS: A TOPOS-THEORETIC PERSPECTIVE DOI : 10.1017/bsl.2015.47
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2016
Priestley-type dualities for partially ordered structures DOI : 10.1016/j.apal.2016.04.008
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2016
Topological Galois theory DOI : 10.1016/j.aim.2015.11.050
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2015
The Morita-equivalence between MV-algebras and lattice-ordered abelian groups with strong unit DOI : 10.1016/j.jalgebra.2014.08.008
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2014
Fraïssé's Construction from a Topos-Theoretic Perspective DOI : 10.1007/s11787-014-0104-6
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2014
Topologies for intermediate logics DOI : 10.1002/malq.201200059
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2014
A general method for building reflections DOI : 10.1007/s10485-013-9300-4
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2012
Syntactic characterizations of properties of classifying toposes
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2012
Universal models and definability DOI : 10.1017/S0305004111000624
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2012
Atomic toposes and countable categoricity DOI : 10.1007/s10485-010-9244-x
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2011
A characterization theorem for geometric logic DOI : 10.1016/j.apal.2010.08.004
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2009
De Morgan classifying toposes DOI : 10.1016/j.aim.2009.07.009
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2009
De Morgan's law and the theory of fields DOI : 10.1016/j.aim.2009.07.019