  The gravity dual of $\beta$-deformed ABJM theory can be obtained by a TsT
transformation of $AdS_4\times\mathbb{CP}^3$. We present a supercoset
construction of $\mathbb{CP}^3$ to obtain this gravity dual theory as a
Yang-Baxter deformation. This is done by selecting a convenient combination of
Cartan generators in order to get an Abelian $r$-matrix satisfying the
classical Yang-Baxter equation. Our results provide another illustration of the
relation between Abelian $r$-matrices and TsT transformations.
