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

Parents:

  • Category theory

    How math­e­mat­i­cal ob­jects are re­lated to oth­ers in the same cat­e­gory.