  We introduce the enveloping algebra for a Leibniz pair, and show that the
category of modules over a Leibniz pair is isomorphic to the category of left
modules over its enveloping algebra. Consequently, we show that the cohomology
theory for a Leibniz pair introduced by Flato, Gerstenhaber and Voronov can be
interpreted by Ext-groups of modules over the enveloping algebra.
