The quotient G / ker ⁡ ⁡ ( F ) ⇉ ⇉ M has a natural groupoid structure such that the projection G → → G / ker ⁡ ⁡ ( F ) is a groupoid morphism; however, unlike quotients of Lie groups, G / ker ⁡ ⁡ ( F ) may fail to be a Lie groupoid in general. Accordingly, the isomorphism theorems for groupoids cannot be specialised to the entire category of Lie groupoids, but only to special classes.