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#### Seminar des SFB/TRR 326 GAUS

„Homotopy Theory in Condensed Mathematics“
The $\infty$-category of condensed anima combines the homotopy theoretic direction of anima with the topological space direction of condensed sets. Hence, it is natural to ask for its role in homotopy theory. In the first part of my talk, I will explain how to assign to every condensed anima a pro-homotopy type by which we also obtain a notion of homotopy pro-groups. Then, I will introduce a refinement of the \'{e}tale homotopy type in the condensed setting. I will explain how this object arises from the nice properties of the pro-\'{e}tale topology and the theory of $\infty$-topoi.