# Kerodon

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Remark 2.5.2.2. Let $\operatorname{\mathcal{C}}$ be a differential graded category. For each object $X \in \operatorname{Ob}(\operatorname{\mathcal{C}})$, the identity morphism $\operatorname{id}_{X}$ is a $0$-cycle of the chain complex $\operatorname{Hom}_{\operatorname{\mathcal{C}}}(X,X)_{\ast }$: that is, it satisfies $\partial (\operatorname{id}_ X) = 0$. This follows from the calculation

$\partial ( \operatorname{id}_ X ) = \partial ( \operatorname{id}_ X \circ \operatorname{id}_ X) = \partial (\operatorname{id}_ X) \circ \operatorname{id}_ X + \operatorname{id}_ X \circ \partial (\operatorname{id}_ X) = \partial (\operatorname{id}_ X) + \partial (\operatorname{id}_ X).$