  In this paper an algebraic model for unbased rational homotopy theory from
the perspective of curved Lie algebras is constructed. As part of this
construction a model structure for the category of pseudo-compact curved Lie
algebras with curved morphisms will be introduced; one which is Quillen
equivalent to a certain model structure of unital commutative differential
graded algebras, thus extending the known Quillen equivalence of augmented
algebras and differential graded Lie algebras.
