Page "Subfunctor" Paragraph 5

For example, let 1 be the category with a single object and a single arrow.

A functor F: 1 → Set maps the unique object of 1 to some set S and the unique identity arrow of 1 to the identity function 1 < sub > S </ sub > on S. A subfunctor G of F maps the unique object of 1 to a subset T of S and maps the unique identity arrow to the identity function 1 < sub > T </ sub > on T. Notice that 1 < sub > T </ sub > is the restriction of 1 < sub > S </ sub > to T. Consequently, subfunctors of F correspond to subsets of S.