Free transitive regular

Let \(\Gg \ltimes X\) be an action of a groupoid object \(\Gg\) on an object \(X \in T\). We say that this action is

1. Free if its shear map \(\shear_1\) is a monomorphism;

2. Transitive if its shear map \(\shear_1\) is an effective epimorphism;

3. Regular if its shear map \(\shear_1\) is an isomorphism.

Note that \(\Gg \ltimes X\) is regular if and only if it is both free and transitive.