Definition 22.25.3. Let $R$ be a ring. Let $\mathcal{A}$ be a graded category over $R$. We let *$\mathcal{A}^0$* be the category with the same objects as $\mathcal{A}$ and with

\[ \mathop{\mathrm{Hom}}\nolimits _{\mathcal{A}^0}(x, y) = \mathop{\mathrm{Hom}}\nolimits ^0_\mathcal {A}(x, y) \]

the degree $0$ graded piece of the graded module of morphisms of $\mathcal{A}$.

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