# nLab bireflective subcategory

category theory

## Applications

#### Notions of subcategory

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 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 15:53:40 by David Corfield (86.187.82.215)