 For any category \(\mathbf{C}\), the notation \(\mathbf{C}(A, B)\) is generally used to denote the set of all morphisms from object \(A\) to object \(B\) in category \(\mathbf{C}\). And the set of all functions from the set \(X\) to the set \(Y\) can be understood as the particular case \(\mathbf{Set}(X, Y)\) of this convention where \(\mathbf{C}\) is taken to be the class \(\mathbf{Set}\) of all sets, which we can think of as discrete algebras, that is, algebras with no structure. A class of algebras along with a specified set of homomorphisms between any two of its members is an instance of a category. The members of the class are called the objects of the category while the homomorphisms are called the morphisms.