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SUMMARY:Fiberwise extensions of localizations and colocalizations [MPIM]
DTSTART:20250203T080000Z
DTEND:20250203T090000Z
DTSTAMP:20260513T134400Z
UID:indico-event-228@math-events.uni-bonn.de
DESCRIPTION:Speakers: Samuel Lavenir (MPIM)\n\nAbstract homotopy theory se
 minar\nIn this talk\, I will discuss the problem of extending functors to 
 fiberwise constructions in the setting of higher topoi. I shall explain th
 e relevance of such extensions both from a practical point of view\, and t
 hrough the lens of the internal logic of the topos. After discussing some 
 known results about fiberwise extensions of localization functors\, we wil
 l focus on the dual situation of cellularizations. We will see that extend
 ing such colocalizations is almost never possible\, and relate our result 
 to classical statements by Chachólski and Hernández\, and to a no-go the
 orem of Shulman in homotopy type theory. Along the way\, emphasis will be 
 put on the pertinence of higher categorical language to formalize the prob
 lem of fiberwise constructions.\n\n\nhttps://math-events.uni-bonn.de/event
 /228/
LOCATION:MPIM\, Vivatsgasse\,  7 - Seminar Room (Max Planck Institute for 
 Mathematics)
URL:https://math-events.uni-bonn.de/event/228/
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