On higher dimensional exact Courant algebroids

For a smooth manifold XX we show an equivalence of categories between the category of OX♯[n]OX♯[n]-extensions of TX♯TX♯ and the category of higher-dimensional exact Courant algebroids on XX. In addition, for any object in the category of R[n]R[n] dg-principal bundles over X♯X♯ we construct its Atiyah algebroid which gives rise to an example of OX♯[n]OX♯[n]-extensions of TX♯TX♯.