Categories and Functors

This lecture explores the process of building a category from a directed graph, focusing on the information encoded by a functor based on the domain category. It delves into examples of categories with varying numbers of objects and discusses the concept of an empty category. The lecture also covers the definition of a composition law to transform a digraph into a category, emphasizing the importance of defining functors and presheaves on spaces. Additionally, it examines the requirements for specifying functors and provides explicit examples of Ab-valued presheaves. Inspired by the fundamental group functor, the lecture concludes by discussing the definition of functors in different contexts.