Natural Transformations and Functors

This lecture introduces the concept of natural transformations and functors in the context of category theory, focusing on the composition and identity properties. It covers examples of natural transformations, including the identity transformation for any functor. The lecture also discusses the category Fun(C, D) of functors from a small category C to a category D, where morphisms are natural transformations. The composition of morphisms in Fun(C, D) is defined based on the composition of natural transformations. The instructor illustrates these concepts with examples and emphasizes the importance of understanding the relationship between functors and natural transformations.