CATEGORIES OF DIAGRAMS

This chapter presents the proof for the Yoneda Lemma, which is probably the single most used result in category theory. It is interesting how often it comes up, especially in view of the fact that it is a straightforward generalization of facts that are fairly easily shown in relation to monoids and posets. The topics discussed include set-valued functor categories, Yoneda embedding, limits in categories of diagrams, colimits in categories of diagrams, exponentials in categories of diagrams, and Topoi. Exercises are provided in the last part of the chapter.

This chapter presents the proof for the Yoneda Lemma, which is probably the single most used result in category theory. It is interesting how often it comes up, especially in view of the fact that it is a straightforward generalization of facts that are fairly easily shown in relation to monoids and posets. The topics discussed include set-valued functor categories, Yoneda embedding, limits in categories of diagrams, colimits in categories of diagrams, exponentials in categories of diagrams, and Topoi. Exercises are provided in the last part of the chapter.