Derived deformation functors, Koszul duality, and Maurer-Cartan spaces
arXiv:2503.05307
Abstract
We summarise the chain of comparisons showing Hinich's derived Maurer-Cartan functor gives an equivalence between differential graded Lie algebras and derived Schlessinger functors on Artinian differential graded-commutative algebras. We include some motivating deformation problems and analogues for more general Koszul dual pairs of operads.
arXiv comment16pp., survey with some new material; v2 final version, to appear in Philosophical Transactions of the Royal Society A