We review relevant concepts from and properties of the categories of sets and of endofunctors on the category of sets relevant to our work. We discuss representable functors on the category of sets, introducing our exponential notation for them, and we state and prove the Yoneda lemma for these with the help of an exercise. We then examine sums (or coproducts) and products of sets and functions through the language of indexed families of sets. In particular, we characterize products of sets in terms of dependent functions, generalizing functions by allowing their codomains to vary depending on their inputs. We study nested sums and products of sets, explaining how distributivity allows us to expand products of sums of sets. By lifting all of this material to endofunctors on the category of sets, and using the fact that its limits and colimits are computed pointwise, we set ourselves up to introduce polynomial functors as sums of representable functors in the next chapter. Throughout the chapter, we emphasize key categorical principles and provide detailed explanations to ensure solid comprehension of these fundamental ideas.