Notions of subcategory
Modalities, Closure and Reflection
A coreflective subcategory is a full subcategory whose inclusion functor has a right adjoint (a cofree functor):
The dual concept is that of a reflective subcategory. See there for more details.
This is (AdamekRosicky, theorem 6.28).
the inclusion of Kelley spaces into Top, where the right adjoint “kelleyfies”
the inclusion of torsion abelian groups into Ab, where the right adjoint takes the torsion subgroup.
the inclusion of groups into monoids, where the right adjoint takes a monoid to its group of units.
- Robert El Bashir, Jiri Velebil, Simultaneously Reflective And Coreflective Subcategories of Presheaves (TAC)
Revised on September 8, 2014 21:59:13
by David Corfield