Self-* is widely considered as a foundation for autonomic computing. The notion of autonomic systems (ASs) and self-* serves as a basis on which to build our intuition about category of ASs in general. In this paper we will specify ASs and self-* and then move on to consider products, coproducts and some universal properties of ASs. All of this material is taken as an investigation of our category, the category of ASs, which we call AS.