Introduction to Category Theory: Categories and Examples

This lecture introduces the theory of categories by presenting various examples, such as the category Ens of sets with applications as morphisms, the category Gr of groups with homomorphisms, and the category Ab of abelian groups. It also covers the category VectK of vector spaces over a field K. The lecture explores the concept of natural composition and the formation of new categories from existing ones. Additionally, it discusses the product of categories and the associativity of compositions. The instructor illustrates these concepts with detailed examples and explanations.