A **weak colimit** for a diagram in a category is a cocone over that diagram which satisfies the existence property of a colimit but not necessarily the uniqueness. The dual concept is a weak limit, see there for more.

For example, a **weakly initial object** in a category, $C$, is such that there is at least one arrow from it to any object in $C$.

Weak adjoint functors along with weak colimits were defined in:

- Paul Kainen,
*Weak adjoint functors*, Mathematische Zeitschrift**122**1 (1971) 1-9 [dml:171575]

Last revised on November 1, 2022 at 12:53:00. See the history of this page for a list of all contributions to it.