Filtered (Co)limit

A cofiltered limit is a limit indexed by a cofiltered category.
A filtered colimit is a colimit indexed by a filtered category.

(Co)filtered Category

Definition

A category $\mathcal{J}$ is filtered when every finite diagram in $\mathcal{J}$ has a cocone.
Dually, $\mathcal{J}$ is cofiltered when every finite diagram in $\mathcal{J}$ has a cone.

Examples

Directed Posets

A directed poset is a non-empty poset in which any two elements have a common upper bound.

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