Lemma 4.18.5. Let $\mathcal{C}$ be a category. The following are equivalent:

1. Connected finite colimits exist in $\mathcal{C}$.

2. Coequalizers and pushouts exist in $\mathcal{C}$.

Proof. Omitted. Hint: This is dual to Lemma 4.18.2. $\square$

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