Math equation demo

In more explicit terms, the equaliser consists of an object E and a morphism eq : E → X satisfying $f\circ eq=g\circ eq$, and such that, given any object O and morphism m : O → X, if $f\circ m=g\circ m$, then there exists a unique morphism u : O → E such that $eq\circ u=m$.

A morphism $m:O\rightarrow X$ is said to equalise $f$ and $g$ if $f\circ m=g\circ m$.