nLab weak colimit

Idea

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 $C$.

Related concepts

• weak limit

• weak multilimit

• WISC

• weakly initial set

• weakly initial object

References

Weak adjoint functors along with weak colimits were defined in:

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