Abstract
We construct Quillen equivalent semi-model structures on the categories of dg-Lie algebroids and L∞-algebroids over a commutative dg-algebra in characteristic zero. This allows one to apply the usual methods of homotopical algebra to dg-Lie algebroids: for example, every Lie algebroid can be resolved by dg-Lie algebroids that arise from dg-Lie
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