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AbstractThe 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 $$E_\infty $$ E ∞ -ring spectra in various ways. In this work we first establish, in the context of $$\infty $$ ∞ -categories and using Goodwillie's calculus of functors, that various definitions of the cotangent complex of a map of $$E_\infty $$ E ∞ -ring spectra that exist in the literature are equivalent. We then turndoi:10.1007/s12188-020-00226-8 fatcat:tezvbl5xyjb4xowfmohbgxw4cy