VB-Hom Algebroid Morphisms and 2-Term Representation Up to Homotopy of Hom-Lie Algebroids

A hom-Lie algebroid is a vector bundle together with a Lie algebroid-like structure which is twisted by a homomorphism and a VB-hom algebroid is essentially defined as a hom-Lie algebroid object in the category of vector bundles. In this paper, we show that, there exists a correspondence between the VB-hom algebroids and two term representations up to homotopy of hom-Lie algebroid.