I will show that Hermitian-Einstein connections can be described as representations of a Lie algebroid, which is defined using the holonomy Lie algebra of the underlying manifold. This naturally leads to the category of derived representations. The theorem by Donaldson, Uhlenbeck and Yau provides a correspondence between the space of Hermitian-Einstein connections and the moduli space of holomorphic vector bundles. The latter carries a natural derived structure. I will try to relate the two derived structures, in particular in the special case of a Calabi-Yau four-fold.