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The cotangent complex of a map of commutative rings is a central object in deformation theory. Since the 1990s, it has been generalized to the homotopical setting of E_∞-ring spectra in various ways. In this work we first establish, in the context of ∞-categories and using Goodwillie's calculus of functors, that various definitions of the cotangent complex of a map of E_∞-ring spectra that exist in the literature are equivalent. We then turn our attention to a specific example. Let R be anarXiv:2005.01382v2 fatcat:pcuelhxdwfd27k2e7pp43udtri