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If $\mathcal{C}$ is a category with all small colimits (i.e., cocomplete), then can we tell that the morphism category $\mathrm{Mor}(\mathcal{C})$ is also cocomplete?

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The arrow category is a functor category $[\mathbb I, \mathcal C]$, where $\mathbb I$ is the interval category. Functor categories inherit colimits from their codomain, so the arrow category is cocomplete when $\mathcal C$ is.

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