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 bimorphism.

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 August 19, 2018 at 04:55:00.
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