symmetric monoidal (∞,1)-category of spectra
In any context of higher algebra where higher central extension make sense, one may ask for the universal such. Since an ordinary universal central extension of some algebraic object is characterized as the initial object in the category of all its ordinary central extensions, an evident definition of universal higher central extension is as a suitable initial object in a higher category of higher central extensions.
For higher central extensions in the context of discrete 2-groups this is considered in Epa-Ganter 16, Def. 2.4
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