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$\gdef\ccal{\mathcal C}$

[N]

section 2.1

By a dg category $\ccal$, we mean a stable differential $\Z$-graded category. The hom complex is a $\Z$-graded cochain complex. We have a shift functor $[n]$ for any $n \in \Z$. 

By a 2-periodic dg category $\ccal$, we mean a $\Z$-graded category that the functor $[2]$ is equivalent to identity. Note that the hom complex is $\Z$-graded.</description>
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