Page "Limit (category theory)" Paragraph 23

Limits and colimits can also be defined for collections of objects and morphisms without the use of diagrams.

The definitions are the same ( note that in definitions above we never needed to use composition of morphisms in J ).

This variation, however, adds no new information.

Any collection of objects and morphisms defines a ( possibly large ) directed graph G. If we let J be the free category generated by G, there is a universal diagram F: J → C whose image contains G. The limit ( or colimit ) of this diagram is the same as the limit ( or colimit ) of the original collection of objects and morphisms.