A category is anything that satisfies this definition—and we will have plenty of examples very soon. For now I want to emphasize that, unlike in Section 1.2, the objects do not have to be sets and the arrows need not be functions. In this sense, a category is an abstract algebra of functions, or “arrows” (sometimes also called “morphisms”), with the composition operation “◦” as primitive. If you are familiar with groups, you may think of a category as a sort of generalized group.