Functors: Examples

This lecture introduces the concept of functors in the context of category theory, focusing on identity functors and forgetful functors. The instructor explains how identity functors preserve the structure of categories, while forgetful functors 'forget' the structure on objects and morphisms. Examples are provided to illustrate how forgetful functors work in different categories, such as groups and vector spaces. The lecture emphasizes the preservation of composition and identities by functors, highlighting the relationship between different categories. Additionally, the lecture discusses how certain categories are subcategories of others, showcasing the hierarchical nature of category theory.