Validity of the internal stabilization characterization of global spectra

Determine whether the characterization of the ∞-category of global spectra as a suitable stabilization internal to modules over the global space category Sgl in PrL is valid.

Background

The paper discusses an announced characterization of the ∞-category of global spectra as a suitable stabilization internal to Sgl-modules in PrL, attributed to Gepner and Nikolaus. The authors explain that the argument supporting that announcement contains a gap and explicitly state that it is unclear whether the original claim is true. Their own universal-property theorem for global spectra is presented as a different result rather than as a resolution of the validity of that earlier characterization.

References

A similar characterization of the ∞-category of global spectra as a suitable stabilization internal to Sgl-modules in PrL had been announced by Gepner and Nikolaus [Nik15]. As we learned from them, their argument contained a gap, and it is not clear whether their original claim is true.

— Global $\infty$-categories and global Thom spectra  (2608.28504 - Brink et al., 28 Aug 2026) in Introduction, p. 7; Remark 7.86