Notation 8.6.9.6. In the situation of Definition 8.6.9.5, the coend of a functor $\mathscr {K}: \operatorname{\mathcal{C}}\times \operatorname{\mathcal{C}}^{\operatorname{op}} \rightarrow \operatorname{\mathcal{D}}$ (if it exists) is uniquely determined up to equivalence and depends functorially on $\mathscr {K}$. To emphasize this dependence, we will denote the coend of $\mathscr {K}$ by $\operatorname{Coend}(\mathscr {K} )$.
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