Kinyon showed that the tangent space of a Lie Rack at the neutral element has
a Leibniz algebra structure. This provided a promising lead towards solving the
Coquecigrue problem for Leibniz algebras. In this paper, we introduce the
category of Lie $n$-racks and generalize several results known on racks. In
particular, we generalize Kinyon's result to Leibniz $n$-algebras.