  Starting from a one dimensional vector space, we construct a categorification
$'\mathcal H$ of a deformed Heiserberg algebra $'H$ by Cautis and Licata's
method. The Grothendieck ring of $'\mathcal H$ is $'H$. As an application, we
discuss some related partition functions related to the MacMahon function of 3D
Young diagram. We expect further applications of the results of this paper.
