Condensed Anima as a Fractured Topos

Clausen-Scholze and Barwick-Haine being the main players in the game, it is no surprise that condensed mathematics has been popular in recent years. They define condensed objects to be sheaves on the category of compact Hausdorff spaces CHaus for quite a simple Grothendieck topology and so it is not far-reaching that this category should inherit various nice structures and properties. In joint work with Nima Rasekh, we realize one such structure, namely we realize the ∞-topos of condensed anima Cond(An) as a fractured ∞-topos in the sense of Carchedi and Lurie.

In this talk, I will give a crash course on condensed mathematics and explain the notion of fractured topoi with the goal of putting a fractured structure on Cond(An). Time permitting, I will give an application by proving that the ∞-topos Cond(An) has enough points.