Natural Transformations: Definition

This lecture introduces the concept of natural transformations between functors, defined as an application between objects and morphisms in different categories, ensuring commutativity of specific diagrams. The instructor explains how to compare functors with the same domain and codomain, illustrating the process through diagrams and mathematical definitions. The lecture also covers the notion of natural isomorphisms, highlighting the conditions under which a natural transformation becomes an isomorphism. By the end of the lecture, students will have a clear understanding of how natural transformations operate and their significance in category theory.