A bireflective subcategory$B\subset C$ is a subcategory which is both reflective and coreflective; i.e. it is a fully faithful functor possesing both left and right adjoints.

Some people use the term in different, weaker meaning, that the unit of the adjunction is a bimorphism.

The adjoint pair induced form the adjoint triple given by reflection, inclusion and coreflection of a bireflective subcategory is an adjoint modality. See there for more.

Revised on March 28, 2015 12:16:42
by Urs Schreiber
(89.15.236.72)