  We comment on the recent paper ``Floquet non-Abelian topological insulator
and multifold bulk-edge correspondence" by Tianyu Li and Haiping Hu, Nat. Comm.
{\bf 14}, 6418 (2023). Apart from the fact that the authors unjustly imply to
study multi-gap topology in Floquet systems for the first time, only known
homotopic relations are presented. While such insights are used to present
interesting Floquet phenomena and phases, which is an attractive result in
itself, they cannot be used to deduce the total bulk characterization in the
dynamical context without further proof. In fact, the authors essentially
rephrase a Zak phase description. These results should in particular be
contrasted to earlier results, arXiv:2208.12824, in which static-compatible Zak
phases {\it and} dynamical Dirac strings were shown to be able to {\it
distinguish} rather similar non-Abelian Floquet phases in $2+1$ dimensional
systems. As a result, the claim of a sharp multifold bulk-edge correspondence
cannot be concluded from the given arguments.
