  In this paper, we relate Lie algebroids to Costello's version of derived
geometry. For instance, we show that each Lie algebroid $L$-and the natural
generalization to dg Lie algebroids-provides an (essentially unique) $L_\infty$
space. More precisely, we construct a faithful functor from the category of Lie
algebroids to the category of $L_\infty$ spaces. Then we show that for each Lie
algebroid $L$, there is a fully faithful functor from the category of
representations up to homotopy of $L$ to the category of vector bundles over
the associated $L_\infty$ space. Indeed, this functor sends the adjoint complex
of $L$ to the tangent bundle of the $L_\infty$ space. Finally, we show that a
shifted-symplectic structure on a dg Lie algebroid $L$ produces a
shifted-symplectic structure on the associated $L_\infty$ space.
