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A Ph.D. thesis by Olivia Caramello on the role of Grothendieck toposes as classifying objects for mathematical theories and logical systems. The thesis explores various applications of …
Grothendieck Toposes as Unifying ‘Bridges’: A Mathematical ...
Feb 24, 2012 · In this paper our aim is to expose some of the philosophical principles underlying our view of Grothendieck toposes as unifying ‘bridges’ between different mathematical …
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Grothendieck toposes as unifying ‘bridges’ in Mathematics. Olivia Caramello. Università degli Studi dell’Insubria (Como) SSLPS Annual Meeting 2018, Lugano 22 September 2018. The …
A. Grothendieck. Topos theory can be regarded as a unifying subject in Mathema-tics, with great relevance as a framework for systematically inves-tigating the relationships between different …
Unifying theory - toposes as 'bridges' - Olivia Caramello
Toposes as 'bridges' General overview. At the beginning of my Ph.D. studies, I had the intuition that Grothendieck toposes could effectively serve as 'bridges' for connecting different …
Grothendieck Toposes as Unifying ‘Bridges’: A Mathematical Morphogenesis. Olivia Caramello. Abstract We present some philosophical principles underlying the theory of topos-theoretic …
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Our methodologies are based on a new view of Grothendieck toposes (in the sense of [1]) as unifying spaces which can serve as “bridges” for transferring information, ideas, and results …
I.1. Grothendieck topologies, sheaves, toposes and points. I.2. Linguistic descriptions of points and first-order geometric theories. I.3. Classifying toposes, toposes as bridges and the …
Grothendieck Toposes as Unifying ‘Bridges’: A ... - ResearchGate
We provide an explicit characterization of the covariant isotropy group of any Grothendieck topos, i.e. the group of (extended) inner automorphisms of any sheaf over a small site.
Grothendieck toposes as unifying 'bridges' in Mathematics
Abstract: I will present a novel view of Grothendieck toposes as unifying spaces in Mathematics being able to effectively serve as 'bridges' for transferring concepts and results across distinct …
A duality theorem | Theories, Sites, Toposes: Relating and …
This chapter presents a duality theorem providing, for each geometric theory, a natural bijection between its geometric theory extensions (also called ‘quotients’) and the subtoposes of its …
Toposes and their place in mathematics: an ... - Istituto …
Apr 1, 2024 · In the interview, given on the occasion of the first edition of the International Congress of Basic Science, she extensively talks about her theory of toposes as “bridges”, …
Toposes as bridges between geometric forms and linguistic …
Feb 18, 2022 · Abstract: It will be shown how any presentation of a Grothendieck topos by a site allows to give a linguistic description of set-based points and generalised points of a topos. …
Olivia Caramello is a mathematician who proposes a new view of Grothendieck toposes as unifying spaces for transferring information between different mathematical theories. Her paper …
The Theory of Topos-Theoretic ‘Bridges’—A Conceptual Introduction
Grothendieck toposes allow us to materialize a tremendous number of ideal objects, and hence to establish effective bridges between a great variety of different contexts. In general, looking for …
The Unification of Mathematics via Topos Theory | SpringerLink
These principles are based on a new view of Grothendieck toposes as unifying spaces being able to act as “bridges” for transferring information, ideas, and results between distinct …
Grothendieck topology | Around toposes
Jan 5, 2024 · The theory of classifying toposes, which was developped by W. Lawvere and the school of categorical logic in the 1970’s, building on some seminal ideas of Grothendieck, was …
Theories, Sites, Toposes: Relating and studying mathematical …
Feb 21, 2018 · Introduces a set of methods and techniques for studying mathematical theories and relating them to each other through the use of Grothendieck toposes.
A course on toposes as ‘bridges’ - Around toposes
Feb 16, 2022 · The theory of classifying toposes, which was developped by W. Lawvere and the school of categorical logic in the 1970’s, building on some seminal ideas of Grothendieck, was …
Alexandre Grothendieck 1928–2014, Part 1 Michael Artin, Allyn …
Alexander Grothendieck: A Country Known Only by Name Pierre Cartier To the memory of Monique Cartier (1932–2007) This article originally appeared in Inference: International …
Glendale-Hyperion Bridge - Wikipedia
The 1910 wooden bridge shortly after it was destroyed by flooding in February of 1927. The Glendale-Hyperion Bridge is a concrete arch bridge viaduct in Atwater Village that spans the …
2003 GUIDELINES FOR THE SEISMIC DESIGN OF HIGHWAY BRIDGES PART I: SPECIFICATIONS MCEER/ATC-49 iii PREFACE PREFACE The 1971 San Fernando …
Next generation seismic fragility curves for California bridges ...
Quantitative and qualitative assessment of the seismic risk to highway bridges is crucial in pre-earthquake planning, and post-earthquake response of transportation systems. Such …
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