Definition 22.25.4. Let $R$ be a ring. Let $\mathcal{A}$ be a graded category over $R$. A direct sum $(x, y, z, i, j, p, q)$ in $\mathcal{A}$ (notation as in Homology, Remark 12.3.6) is a graded direct sum if $i, j, p, q$ are homogeneous of degree $0$.

In your comment you can use Markdown and LaTeX style mathematics (enclose it like $\pi$). A preview option is available if you wish to see how it works out (just click on the eye in the toolbar).