From $L_\infty$ algebroids to $L_\infty$ spaces: Part I

The notion of $L_\infty$ spaces over dg manifolds is developed.

An equivalence between the category of transitive $L_\infty$ algebroids and that of $L_\infty$ spaces is established, and this equivalence detects weak equivalences.

Moreover, a faithful functor from $L_\infty$ algebroids to $L_\infty$ spaces is constructed, which also detects weak equivalences.