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PRODID:-//Memento EPFL//
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SUMMARY:Structured Geometric Sheaves in Higher Category Theory
DTSTART:20220315T101500
DTEND:20220315T111500
DTSTAMP:20260407T143639Z
UID:388d7a301749644b30bd23650b998fc8ab436fb02dc4c66087723663
CATEGORIES:Conferences - Seminars
DESCRIPTION:Raffael Stenzel\, Masaryk University\nMuch like ordinary topos
  theory is the theory of sheaves on a category equipped with a topology\, 
 higher topos theory can be understood as the theory of homotopy-coherent s
 heaves on a higher category equipped with a "structured" topology. In esse
 nce\, the latter notion replaces coherent families of covering sieves with
  coherent families of fibered covering structures.\n\nIn this talk we make
  use of that additional freedom in the definition of higher sites to move 
 away from the classical sheaf condition over topological spaces -- and ove
 r geometric categories more generally -- and introduce a stronger limit-pr
 eserving property. We therefore define and study a new class of higher top
 oses: the structured geometric sheaf theories on suitably equipped higher 
 categories. We will see that the two notions of structured and unstructure
 d (i.e. ordinary) geometric sheaves differ only by a subtle cotopological 
 fragment. Yet it turns out that this fragment is crucial in various aspect
 s. As a case in point\, we will show that every higher topos is the theory
  of structured geometric sheaves over itself\, while the same is generally
  not true for the ordinary geometric sheaves over itself.
LOCATION:MA A3 30 https://plan.epfl.ch/?room==MA%20A3%2030
STATUS:CONFIRMED
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