Abstract Anel

Title: New methods for left exact localizations of topoi.

 Abstract: This talk will be around the following question: given a map f in a topos E, how to describe the left exact localization forcing f to become an isomorphism ?

The classical answer is to generate an explicit (Grothendieck or Lawvere-Tierney) topology. But in the context of infinity-topoi, not every left exact localization is controlled by a topology.

I will recall why and give a new explicit description of the left exact localisation generated by f.

I will finish by presenting an alternative to the notion of site, best suited for infinity-topoi. This is part of a joint work with G. Biedermann, E. Finster & A. Joyal.

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