Equaliser (category theory)

In Category theory, an equaliser of a pair of arrows $~$f, g: A \to B$~$ is an object $~$E$~$ and a universal arrow $~$e: E \to A$~$ such that $~$ge = fe$~$. Explicitly, $~$ge = fe$~$, and for any object $~$X$~$ and arrow $~$x: X \to A$~$ such that $~$fx = gx$~$, there is a unique factorisation $~$\bar{x} : X \to A$~$ such that $~$e \bar{x} = x$~$.