  Let $(\mathcal{A,B})$ be a GP-admissible pair and $(\mathcal{Z,W})$ be a
GI-admissible pair of classes of objects in an abelian category $\mathcal{C}$,
and consider the class $\pi\mathcal{GP}_{(\omega,\mathcal{B},1)}$ of
$1$-periodic $(\omega,\mathcal{B})$-Gorenstein projective objects, where
$\omega := \mathcal{A} \cap \mathcal{B}$ and $\nu := \mathcal{Z} \cap
\mathcal{W}$. We claimed in \cite[Lem. 8.1]{HMP2023m} that the
$(\mathcal{Z,W})$-Gorenstein injective dimension of
$\pi\mathcal{GP}_{(\omega,\mathcal{B},1)}$ is bounded by the
$(\mathcal{Z,W})$-Gorenstein injective dimension of $\omega$, provided that:
(1) $\omega$ is closed under direct summands, (2)
$\mathrm{Ext}^1(\pi\mathcal{GP}_{(\omega,\mathcal{B},1)},\nu) = 0$, and (3)
every object in $\pi\mathcal{GP}_{(\omega,\mathcal{B},1)}$ admits a
$\mathrm{Hom}(-,\nu)$-acyclic $\nu$-coresolution. These conditions are their
duals are part of what we called ``Setup 1''. Moreover, if we replace
$\pi\mathcal{GP}_{(\omega,\mathcal{B},1)}$ by the class
$\mathcal{GP}_{(\mathcal{A,B})}$ of $(\mathcal{A,B})$-Gorenstein projective
objects, the resulting inequality is claimed to be true under a set of
conditions named ``Setup 2''.
  The proof we gave for the claims
$\mathrm{Gid}_{(\mathcal{Z,W})}(\pi\mathcal{GP}_{(\omega,\mathcal{B},1)}) \leq
\mathrm{Gid}_{(\mathcal{Z,W})}(\omega)$ and
$\mathrm{Gid}_{(\mathcal{Z,W})}(\mathcal{GP}_{(\mathcal{A,B})}) \leq
\mathrm{Gid}_{(\mathcal{Z,W})}(\omega)$ is incorrect, and the purpose of this
note is to exhibit a corrected proof of the first inequality, under the
additional assumption that every object in
$\pi\mathcal{GP}_{(\omega,\mathcal{B},1)}$ has finite injective dimension
relative to $\mathcal{Z}$. Setup 2 is no longer required, and as a result the
second inequality was removed. We also fix those results in \S \ 8 of
\cite{HMP2023m} affected by Lemma 8.1, and comment some applications and
examples.
