Definition:Filtered Category

Definition

Let $\mathbf I$ be a category.

$\mathbf I$ is filtered, when:

$\mathbf I$ is not empty

For every two objects $i$ and $i'$ of $\mathbf I$, there exists an object $k$ and morphisms $f: i \to k$ and $f' : i' \to k$

For every two objects $i$ and $j$ of $\mathbf I$ and every two morphisms $u : i \to j$ and $v : i \to j$, there exists an object $k$ a morphism $w : j \to k$, such that $w \circ u = w \circ v$.

Sources

There are no source works cited for this page. Source citations are highly desirable, and mandatory for all definition pages. Definition pages whose content is wholly or partly unsourced are in danger of having such content deleted. To discuss this page in more detail, feel free to use the talk page.