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

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

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.
$\square$

Your email address will not be published. Required fields are marked.

In your comment you can use Markdown and LaTeX style mathematics (enclose it like `$\pi$`

). A preview option is available if you wish to see how it works out (just click on the eye in the toolbar).

Unfortunately JavaScript is disabled in your browser, so the comment preview function will not work.

All contributions are licensed under the GNU Free Documentation License.

## Comments (2)

Comment #2352 by MAO Zhouhang on

Comment #2419 by Johan on

There are also: