  These notes are an expanded version of my talk at the ICRA 2018 in Prague,
Czech Republic; they are based on joint work with Tobias Dyckerhoff and Tashi
Walde. In them we relate Iyama's higher Auslander algebras of type $\mathbb{A}$
to Eilenberg--Mac Lane spaces in algebraic topology and to higher-dimensional
versions of the Waldhausen $\operatorname{S}$-construction from algebraic
$K$-theory.
