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.)

See also

• Pointed category

References

• Pitts, Andrew M. (2013). Nominal Sets: Names and Symmetry in Computer Science. Cambridge Tracts in Theoretical Computer Science. Vol. 57. Cambridge University Press. p. 16. ISBN 978-1107017788.