Topological spaces and simplicial sets have associated homotopy types (that is, the 1-category of topological spaces maps to the infinity-category of spaces, and so does the 1-category of simplicial sets), but these are not the only kind of mathematical objects that have associated homotopy types. In this talk, I will present a mathematical object (not a topological

space) that comes from the theory of von Neumann algebras, and whose associated homotopy type is K(Z,4).