  A more direct example is provided by the power set operation, which yields two functors on the category of sets, depending on how one defines its action on functions. Thus given a set \(X, \wp(X)\) is the usual set of subsets of \(X\), and given a function \(\boldsymbol{f}: X \rightarrow Y, \wp(\boldsymbol{f}): \wp(X) \rightarrow \wp(Y)\) takes a subset \(A\) of \(X\) and maps it to \(B = \boldsymbol{f}(A)\), the image of \(\boldsymbol{f}\) restricted to \(A\) in \(X.\) It is easily verified that this defines a functor from the category of sets into itself.