filtered category

Let \(\mathcal{C}\) be a category. Then \(\mathcal{C}\) is said to be filtered, if for any two objects \(j_1,j_2\)

1. and parallel morphisms \(f,g: j_1 \rightarrow j_2\) there exists a cofork
2. for any two objects \(j',j'\) there exists an object \(k\) and morphisms \(j \rightarrow k, j' \rightarrow k\)
3. and \(\mathrm{Ob}(\mathcal{C})\) is nonempty