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We use a "twisted group algebra" method to constructively adjoin formalradicals $\sqrt[n]{\alpha}$, for $\alpha$ a unit in a commutative ring spectrumor an invertible object in a symmetric monoidal $\infty$-category. We show thatthis construction is classified by maps from Eilenberg-Mac Lane objects to theunit spectrum, the Picard spectrum, and the Brauer spectrum.

Adjoining roots in homotopy theory