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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