Lie maps of Lie algebras are dual to linear Poisson maps of the dual Poisson manifolds. Higgins & Mackenzie proved an analogous result for Lie algebroids and Poisson bundles using comorphisms of Lie algebroids, a concept they introduced. After reviewing this result, we introduce the notion of an L-infinity comorphism, explore some of its properties, and show that it extends the correspondence of Higgins-Mackenzie to higher bracket structures. Based on joint work with T. Voronov.