Moduli Problems for Ring Spectra

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Derived Algebraic Geometry (2014, background): “By the main theorem of [88], lx determines a unique ∞-functor Fx : dgartk −→ S, where dgart ∗ k is the ∞-category of locak augmented commutative dg-algebras over k with finite dimensional total homotopy (also called artinian commutative dg-algebras over k).”
Derived algebraic geometry (2014, background): “By the main theorem of [88], lx determines a unique ∞-functor Fx : dgartk −→ S, where dgart ∗ k is the ∞-category of locak augmented commutative dg-algebras over k with finite dimensional total homotopy (also called artinian commutative dg-algebras over k).”
A geometric construction of the Witten genus, I (2010, background): “formal moduli problem is a functor F from the category of nilpotent dg algebras over k to the category of simplicial sets, such that F(k) is contractible, and F preserves certain homotopy limits. See [Lur10] for more details. We want to explain brieﬂy how every L¥ algebra ggives rise to a formal mod”