Well-pointed category

In category theory, a category with a terminal object $$1$$ is well-pointed if for every pair of arrows $$f,g:A\to B$$ such that $$f\neq g$$, there is an arrow $$p:1\to A$$ such that $$f\circ p\neq g\circ p$$. (The arrows $$p$$ 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.)