representation, ∞-representation?
symmetric monoidal (∞,1)-category of spectra
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on the notions of deformation theory – such as Kähler differentials and cotangent complexes – generalized from the ordinary context of algebra to that of higher algebra. In particular it studies the case where ordinary commutative rings are refined to by $E_\infty$-rings. See also at E-∞ geometry.
Much of this has meanwhile be absorbed in section 8.3 of
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