A bireflective subcategory$B\subset C$ 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 monomorphism and epimorphism.

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

Last revised on November 5, 2021 at 09:49:04.
See the history of this page for a list of all contributions to it.