Homotopy theory for curved $L_{\mathrm{\infty }}$ spaces

This paper proves that $L_{\mathrm{\infty }}$ spaces over a dg manifold form a category of fibrant objects. Together with the first main result of the companion paper [CJ26], this implies that transitive $L_{\mathrm{\infty }}$ algebroids over a dg manifold also form a category of fibrant objects.