  When $\mathbb C$ is a semi-abelian category, it is well known that the
category $\mathsf{Grpd}(\mathbb C)$ of internal groupoids in $\mathbb C$ is
again semi-abelian. The problem of determining whether the same kind of
phenomenon occurs when the property of being semi-abelian is replaced by the
one of being action representable (in the sense of Borceux, Janelidze and
Kelly) turns out to be rather subtle. In the present article we give a
sufficient condition for this to be true: in fact we prove that the category
$\mathsf{Grpd}(\mathbb C)$ is a semi-abelian action representable algebraically
coherent category with normalizers if and only if $\mathbb C$ is a semi-abelian
action representable algebraically coherent category with normalizers. This
result applies in particular to the categories of internal groupoids in the
categories of groups, Lie algebras and cocommutative Hopf algebras, for
instance.
