# 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.