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

Unbased rational homotopy theory: a Lie algebra approach