A model structure for the Goldman-Millson theorem

Abstract

By a result of Vallette, we put a sensible model structure on the category of conilpotent Lie coalgebras. This gives us a powerful tool to study the subcategory of Lie algebras obtained by linear dualization, also known as the category of pronilpotent Lie algebras. This way, we recover weaker versions of the celebrated Goldman-Millson theorem and Dolgushev-Rogers theorem by purely homotopical methods. We explore the relations of this procedure with the existent literature, namely the works of Lazarev-Markl and Buijs-F\'elix-Murillo-Tanr\'e.