Well-pointed category

In category theory, a category with a terminal object [math]\displaystyle{ 1 }[/math] is well-pointed if for every pair of arrows [math]\displaystyle{ f,g:A\to B }[/math] such that [math]\displaystyle{ f\neq g }[/math], there is an arrow [math]\displaystyle{ p:1\to A }[/math] such that [math]\displaystyle{ f\circ p\neq g\circ p }[/math]. (The arrows [math]\displaystyle{ p }[/math] 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. 57. Cambridge University Press. p. 16. ISBN 1107017785.