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 $e \bar{x} = x$.