  The theory of condensed mathematics by Dustin Clausen and Peter Scholze
claims that topological spaces should be replaced by the definition of
condensed sets. The main purpose of this paper is to investigate in which way
the theory of homotopy groups on topological spaces can be extended to the
theory of condensed sets. We show that there exist functors from the category
of condensed sets to the category of pro-groups, s.t. restriction to CW-spaces
coincides with the ordinary notion of homotopy groups on topological spaces.
These functors can be extended to the $\infty$-categories of condensed anima
and pro-anima. On our way to these results we will prove that the compact
projective objects in the category of condensed sets are given by the
extremally disconnected profinite sets.
