# 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.