A category is said to be small if the classes of both its objects and its morphisms are sets. A category that is not small is said to be large. A category ℭ is locally small if for any pair of objects A and B of ℭ the class Homℭ(A,B) is a set. Many of the categories we will consider in this book (the categories of sets, groups, rings, modules over a ring, sheaves on a topological spaces, etc.) are locally small.