coreflective subcategory
Geoff Vooys
A coreflective subcategory is a full subcategory whose inclusion functor has a right adjoint (a cofree functor):
The dual concept is that of a reflective subcategory. See there for more details.
(equivalent characterizations)
Given any pair of adjoint functors
the following are equivalent:
The left adjoint is fully faithful. (In this case is equivalent to its essential image in under , a full coreflective subcategory of .)
The unit of the adjunction is a natural isomorphism of functors.
The...