Natural transformations

Category theory as higher order mathematics exhibits interesting new phenomena that do not arise when you study groups, topology etc alone. The notion of natural transformations is one such example, where there are now "homomorphisms" between "homomorphisms", that is, natural transformations between functors. In any particular category, you have the notion of isomorphism of objects, but now in category theory, you have isomorphisms of "homomorphisms" (as well as isomorphisms of objects). This concept highlights a fundamental difference between category and other branches of mathematics. In this video, we define the concept and give simple examples.