Cat may actually be regarded as a 2-category with natural transformations serving as 2-morphisms.
[1] The terminal object is the terminal category or trivial category 1 with a single object and morphism.
In order to avoid problems analogous to Russell's paradox one cannot form the “category of all categories”.
The category Cat has a forgetful functor U into the quiver category Quiv: This functor forgets the identity morphisms of a given category, and it forgets morphism compositions.
This category theory-related article is a stub.