We explore other large categories based on the category of sets and functions. We begin with monoids, and think of them as sets with extra structure. We introduce the concept of a structure-preserving function, which in this case gives us the definition of a monoid morphism. We check that we can assemble monoids and their morphisms into a category. We do the analogous construction for groups and group homomorphisms. We consider partially ordered sets and show how the structure-preserving functions in this case are order-preserving functions, and we assemble those into a category. We consider some cases of functions that are not order-preserving, illuminating some antagonism that can arise over the theory of privilege. We present the category of topological spaces and continuous maps. We introduce the idea of assembling categories themselves into a category, beginning to think about the idea of structure-preserving maps for categories. These are called functors, and are covered in full in a later chapter. Finally, we touch on matrices, introducing a category where the objects are natural numbers and a morphism from a to b is an a × b matrix. This concludes the interlude of the book.