Extra Material
It is easy to define an isomorphism in a category: it is the one that has an inverse. That is, if we havef: a → bandg: b → a, and f ° g = idband g ° f = ida. We will need this notion later on. A monomorphism and an epimorphim could be also defined, but it takes more efforts, and we are not going to cover them here.

Remember [0..N] objects from the previous page? There are two special categories, 1 = [0], and 2 = [0..1]. The first one has just one object and one morphism; the second one has two objects and three morphisms.

Do categories themselves form a category? They would, but we need to define arrows between categories. That's the second order arrows, and they are called functors.