The Stacks project

Lemma 12.19.11. Let $\mathcal{A}$ be an abelian category. Let $A, B, C \in \text{Fil}(\mathcal{A})$. Let $f : B \to A$ and $g : C \to A$ be morphisms. Then there exists a fibre product

\[ \xymatrix{ B \times _ A C \ar[r]_{g'} \ar[d]_{f'} & B \ar[d]^ f \\ C \ar[r]^ g & A } \]

in $\text{Fil}(\mathcal{A})$. If $f$ is strict, so is $f'$.

Proof. This lemma is dual to Lemma 12.19.10. $\square$

Comments (2)

Comment #2352 by MAO Zhouhang on

Just a typo: The conclusion should be: Then there exists a pullback

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  • 6 comment(s) on Section 12.19: Filtrations

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