On Jacobi quasi-Nijenhuis algebroids and Courant–Jacobi algebroid morphisms

We propose a definition of a Jacobi quasi-Nijenhuis algebroid and show that any such Jacobi algebroid has an associated quasi-Jacobi bialgebroid. Therefore, an associated Courant–Jacobi algebroid is also obtained. We introduce the notions of quasi-Jacobi bialgebroid morphism and Courant–Jacobi algebroid morphism, also providing some examples of Courant–Jacobi algebroid morphisms.