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.

The talk was recorded and the recording can be found here.