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Nima Rasekh: An Example of an Elementary Higher Topos that is not a Grothendieck Higher Topos

Tid: On 2020-01-08 kl 10.00 - 11.45

Plats: Kräftriket, house 5, room 16

Medverkande: Nima Rasekh, École polytechnique fédérale de Lausanne


The theory of Grothendieck higher toposes has been developed quite extensively, which has led to many interesting examples, from sheaves on smooth schemes to 1-excisive functors.

On the other hand, the generalization of Grothendieck higher toposes, namely elementary higher toposes, is a recent development and as of now lacked interesting examples that would demonstrate the additional theoretical strength.

The goal of this talk is to give a class of examples of elementary higher toposes that are not Grothendieck higher toposes, via the filter quotient construction. If time permits, we will focus on one example and show how its non-standard natural number object leads to non-standard truncation levels.