On $\Delta^0_2$-Categoricity of Boolean Algebras

We prove that the notions of $\Delta^0_2$-categoricity and relative $\Delta^0_2$-categoricity in Boolean algebras coincide. As a corollary, we obtain that for every Turing degree $\mathbf{d}<\mathbf{0}'$ a computable Boolean algebra is $\mathbf{d}$-computably categorical if and only if it is computably categorical.