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 \(e \bar{x} = x\).