In mathematics, a pointed set is a set with a distinguished element , which is called the basepoint. Maps of pointed sets (based maps) are those functions that map one basepoint to another, i.e. a map such that . This is usually denoted
There is a faithful functor from usual sets to pointed sets, but it is not full, and these categories are not equivalent.
- Grégory Berhuy (2010). An Introduction to Galois Cohomology and Its Applications. London Mathematical Society Lecture Note Series 377. Cambridge University Press. p. 34. ISBN 0-521-73866-0.
- Mac Lane, Saunders (1998). Categories for the Working Mathematician (2nd ed.). Springer-Verlag. ISBN 0-387-98403-8.