# Well-pointed category

In category theory, a category with a terminal object ${\displaystyle 1}$ is well-pointed if for every pair of arrows ${\displaystyle f,g:A\to B}$ such that ${\displaystyle f\neq g}$, there is an arrow ${\displaystyle p:1\to A}$ such that ${\displaystyle f\circ p\neq g\circ p}$. (The arrows ${\displaystyle p}$ are called the global elements or points of the category; a well-pointed category is thus one that has "enough points" to distinguish non-equal arrows.)