Lemma 4.18.5 (04AV)—The Stacks project

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Table of contents
Part 1: Preliminaries
Chapter 4: Categories
Section 4.18: Finite limits and colimits
Lemma 4.18.5 (cite)

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

Connected finite colimits exist in $\mathcal{C}$ .
Coequalizers and pushouts exist in $\mathcal{C}$ .

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

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