Page "Concrete category" Paragraph 17

# The category Set < sup > op </ sup > can be embedded into Rel by representing each set as itself and each function f: X → Y as the relation from Y to X formed as the set of pairs ( f ( x ), x ) for all x ∈ X ; hence Set < sup > op </ sup > is concretizable.

The forgetful functor which arises in this way is the contravariant powerset functor Set < sup > op </ sup > → Set.