examples of adjoint functors
This entry lists examples for pairs of adjoint functors.
For examples of the other universal constructions see
The classical examples of pairs of adjoint functors are where the right adjoint forgets structure in that it is a faithful functor. In these case the left adjoint usually is the free functor that “adds structure freely”.
In fact, one usually turns this around and defines the free -structure on an object of as the image of that object under the left adjoint (if it exists) to the functor that forgets this structure.
- forgetful right adjoint Grp Set forgets the group structure on a group and just remembers the underlying set – the left adjoint sends each set to the free group over it.
Nerves and realization
For a category equipped with cosimplicial objects and tensored over ;
Revised on October 12, 2010 15:36:40
by David Corfield