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Moduli Problems and DG-Lie Algebras

This entry is about the notes

• Jacob Lurie, Moduli Problems and DG-Lie Algebras (pdf)

This establishes a statement (theorem 5.3) that characterizes ∞-stacks (over an (∞,1)-site of formal duals of E-∞ algebras over a field) such that

1. they have a contractible underlying ∞-groupoid

   $$\Gamma X\simeq *$$\Gamma X \simeq *

   (in the terminology and notation for cohesive (∞,1)-toposes)

2. and respect (∞,1)-pullbacks

with those associated to an ∞-Lie algebra $𝔤$ in the sense of

• Vladimir Hinich, DG coalgebras as formal stacks (arXiv:math/9812034)

The construction is then generalized to noncommutative geometry.

category: reference