  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.
