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Added a (sketchy) pointer to
Thanks for the pointer.
It seems to have gone largely unrecognized that the cohesive $\infty$-topos-theoretic discussion of the String 2-group is in section 5.1.4 of dcct (p. 583).
Reading that sounds as though the $A$ of the extension could be anything, but it’s limited to being homotopy equivalent to $B U(1)$, right?
Triple adjunction rather than adjoint quadruple, hmm.
Yes, on p. 29-30:
[ our definition ] is a generalisation as well as a weakening of the following approach to smooth string group extensions (see, for instance, [FRS16]):
Ok, so have added
with $A$ not necessarily chosen to be $\mathbf{B}U(1)$ but only of the same homotopy type, …
By the way, I think this perspective that the String 2-group, even in the smooth case, “was defined” to be a 3-connected cover is misled:
By it’s very name, the String 2-group is meant to be that $G$ such that $G$-structure encodes cancellation of the Green-Schwarz anomaly.
That for the global GS anomaly (i.e. disregarding differential structure) this is given by a 3-connected cover of the homotopy type pf $Spin$ is a noteworthy phenomenon, but not the definition.
added publication data for:
added publication data for:
To add
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