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SUMMARY:A Functorial Excursion between Algebraic Geometry and Linear Logic
(in person)
DTSTART;VALUE=DATE-TIME:20211201T095000Z
DTEND;VALUE=DATE-TIME:20211201T104000Z
DTSTAMP;VALUE=DATE-TIME:20220810T073354Z
UID:indico-contribution-5974@indico.math.cnrs.fr
DESCRIPTION:Speakers: Paul-André Melliès (CNRS\, Université de Paris)\n
In this talk\, I will use the functor of points approach to Algebraic Geom
etry to establish that every covariant presheaf X on the category of commu
tative rings — and in particular every scheme X — comes equipped “ab
ove it” with a symmetric monoidal closed category PshModX of presheaves
of modules. This category PshModX defines moreover a model of intuitionist
ic linear logic\, whose exponential modality is obtained by glueing togeth
er in an appropriate way the Sweedler dual construction on ring algebras.
The purpose of this work is to explore the idea that linear logic is a log
ic of generalised vector bundles\, in the same way as dependent type theor
y is understood today as a logic of spaces up to homotopy.\n\nhttps://indi
co.math.cnrs.fr/event/7040/contributions/5974/
LOCATION:Le Bois-Marie Centre de conférences Marilyn et James Simons
URL:https://indico.math.cnrs.fr/event/7040/contributions/5974/
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