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We comment on the recent paper ``Floquet non-Abelian topological insulatorand 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 tostudy multi-gap topology in Floquet systems for the first time, only knownhomotopic relations are presented. While such insights are used to presentinteresting Floquet phenomena and phases, which is an attractive result initself, they cannot be used to deduce the total bulk characterization in thedynamical context without further proof. In fact, the authors essentiallyrephrase a Zak phase description. These results should in particular becontrasted to earlier results, arXiv:2208.12824, in which static-compatible Zakphases {\it and} dynamical Dirac strings were shown to be able to {\itdistinguish} rather similar non-Abelian Floquet phases in $2+1$ dimensionalsystems. As a result, the claim of a sharp multifold bulk-edge correspondencecannot be concluded from the given arguments.

Comment on "Floquet non-Abelian topological insulator and multifold bulk-edge correspondence"