Fractured structures on condensed anima

Speaker: Qi Zhu – University of Bonn

Abstract: We compare notions generalizing features of topology, namely condensed mathematics and cohesive resp. fractured structures on topoi. After introducing/recalling the theory of condensed mathematics and cohesive resp. fractured topoi, we discuss their interrelations. Once we have seen that cohesion is not sensible on the $\infty$-topos of condensed anima $\mathbf{Cond(An)}$ we provide a fractured structure on $\mathbf{Cond(An)}$. We apply this to compare sheaf cohomology and condensed cohomology and show that for the corporeal objects of the fractured structure which are also topological spaces the cohomologies agree.