Weak Limit

Idea

In category theory, A weak (co)limit is the extension of the categorical definiton to (co)limit, still requiring all other (co)cones to factor into the limit, but lifting the uniqueness requirement.

Definition

Let $C$ be a category and $D:I\Rightarrow \mathcal{C}$ be a diagram. Then a weak limit is a weak terminal object in the category of $D$-cones. Dually, a weak colimit is a weakly-initial object of the category of $D$-cocones.

See also

Limit (Category Theory)

References

https://ncatlab.org/nlab/show/weak+limit