The Stacks project

Lemma 4.19.3. Let $\mathcal{I}$ be a category. Let $\mathcal{J}$ be a full subcategory. Assume that $\mathcal{I}$ is filtered. Assume also that for any object $i$ of $\mathcal{I}$, there exists a morphism $i \to j$ to some object $j$ of $\mathcal{J}$. Then $\mathcal{J}$ is filtered and cofinal in $\mathcal{I}$.

Proof. Omitted. Pleasant exercise of the notions involved. $\square$

Comments (1)

Comment #9750 by on

For reference, this is Kashiwara, Schapira, Categories and Sheaves, Proposition 3.2.4.

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  • 5 comment(s) on Section 4.19: Filtered colimits

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