$U \underoverset{b}{a}{\rightrightarrows} V \overset{c}{\rightarrow} X$

is called a coequalizer diagram if

$c a=c b$; and

$c$ is universal for this property: i.e. if $f: V \to Y$ is a morphism of $C$ such that $f a=f b$, then there is a unique morphism $f': X \to Y$ such that $f'c=f$.

This concept is a special case of that of colimit; specifically, it’s the colimit of the diagram