The Stacks project

Lemma 4.18.7. Let $\mathcal{C}$ be a category. The following are equivalent:

  1. Finite colimits exist in $\mathcal{C}$.

  2. Finite coproducts and coequalizers exist in $\mathcal{C}$.

  3. The category has an initial object and pushouts exist.

Proof. Omitted. Hint: This is dual to Lemma 4.18.4. $\square$

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