nLab
bireflective subcategory

A bireflective subcategory BCB\subset C is a subcategory which is both reflective and coreflective; i.e. it is a fully faithful functor possessing 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.

Last revised on March 28, 2015 at 15:53:40. See the history of this page for a list of all contributions to it.