A category is complete if every diagram in C has a limit in C.
|This means that arrows between the same objects must have a limit so does this mean the arrows are the same (upto isomorphism)?|
Theorem: If C has a terminal object and a pullback for each pair of C-arrows with common codomain then C is finitely complete.
See Pullback .
Other Meanings of Completeness
In order theory, completeness properties assert the existence of certain infima or suprema of a given partially ordered set (poset)