Morita Invariance of Intrinsic Characteristic Classes of Lie Algebroids

In this note, we prove that intrinsic characteristic classes of Lie algebroids — which in degree one recover the modular class — behave functorially with respect to arbitrary transverse maps, and in particular are weak Morita invariants. In the modular case, this result appeared in [Kosmann-Schwarzbach Y., Laurent-Gengoux C., Weinstein A., Transform. Groups 13 (2008), 727–755], and with a connectivity assumption which we here show to be unnecessary, it appeared in [Crainic M., Comment. Math. Helv. 78 (2003), 681–721] and [Ginzburg V.L., J. Symplectic Geom. 1 (2001), 121–169].