Coequalizer

Summary

The coequalizer of two parallel morphisms $f, g \colon X \to Y$ in a category is a universal morphism $q \colon Y \to Q$ with $q \circ f = q \circ g$. It is the colimit of the diagram formed by $f$ and $g$, and it is dual to the equalizer. In sets it is the quotient of $Y$ that identifies $f(x)$ with $g(x)$ for each $x$. In abelian groups it is the cokernel of $f - g$.