Equaliser (category theory)

In , 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 $\overline{x}:X\to A$ such that $e\overline{x}=x$.