Categorification of $ \mathsf{VB} $-Lie algebroids and $ \mathsf{VB} $-Courant algebroids

<abstract><p>In this paper, first we introduce the notion of a $ \mathsf{VB} $-Lie 2 $-algebroid, which can be viewed as categorification algebroid. The tangent prolongation Lie $-algebroid is naturally. We show that after choosing splitting, there one-to-one correspondence between $-algebroids and flat superconnections 2-algebroid on 3-term complex vector bundles. Then $-$ \mathsf{CLWX} 2-algebroid, $-Courant split 3-algebroids 2-algebroids. Finally, an E associated to structure graded fat bundle By result, give construction new 3-algebra from given 3-algebra, provides interesting examples 3-algebras including higher analogue string 2-algebra.</p></abstract>