  In this paper, we define the notion of Hopf crossed square for cocommutative
Hopf algebras extending the notions of crossed squares of groups and of Lie
algebras. We prove the equivalence between the category of Hopf crossed squares
and the category of double internal groupoids in the category of cocommutative
Hopf algebras. The Hopf crossed squares turn out to be the internal crossed
modules in the category of crossed modules in the category of cocommutative
Hopf algebras.
