As seen above, properness for Lie groupoids is the "right" analogue of compactness for Lie groups. One could also consider more "natural" conditions, e.g. asking that the source map s : G → → M is proper (then G ⇉ ⇉ M is called s-proper), or that the entire space G is compact (then G ⇉ ⇉ M is called compact), but these requirements turns out to be too strict for many examples and applications.