How a Java 8 Stream acts as a Functor

Example.java

package au.id.bje.functor;

import java.util.function.Function;
import java.util.stream.Stream;

public class Example {
    static class A {}
    static class B {}
    static class C {}

    static B aToB(A a) { return new B(); }
    static C bToC(B b) { return new C(); }
    static Function<Stream<A>, Stream<B>> streamAToStreamB
            = streamA -> streamA.map(Example::aToB);
    static Function<Stream<B>, Stream<C>> streamBToStreamC
            = streamA -> streamA.map(Example::bToC);
    static Function<Stream<A>, Stream<C>> streamAtoStreamC
            = streamA -> streamBToStreamC.apply(streamAToStreamB.apply(streamA));

    static Function<Stream<A>, Stream<C>> streamAtoStreamC2
            = streamA -> streamA.map(a -> bToC(aToB(a)));
}