lly:
|
| 16.  Definition.  Let C be a category.  A 'subcategory' D of C is
|      given by a subclass ob(D) of ob(C) and, for each X, Y in ob(D),
|      a subset D(X, Y) of C(X, Y) subject to the axioms that id_X is
|      in D(X, X) and, whenever f is in D(X, Y) and g is in D(Y, Z),
|      then gf in C(X, Z) is in fact in D(X, Z).
|
| It is obvious that such D, with the composition inherited
| from C, satisfies axioms (a, b, c) of the definition of
| a category.  Thus, a subcategory is a category in its
| 