Derived deformation functors, Koszul duality, and Maurer-Cartan spaces

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.

Publication Details

Journal
ArXiv.org
Published
2025-03-07
Primary Topic
Homotopy and Cohomology in Algebraic Topology
Type
article
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article

Derived deformation functors, Koszul duality, and Maurer-Cartan spaces

ArXiv.org
Homotopy and Cohomology in Algebraic Topology
article

Derived deformation functors, Koszul duality, and Maurer-Cartan spaces

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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.org
Openalex Percentile: Top 44%
Homotopy and Cohomology in Algebraic Topology
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Derived deformation functors, Koszul duality, and Maurer-Cartan spaces · ArXiv.org (2025) | TGRS Research Map | TGRS