The thing about inheritance is it limits you to one relation. Composition is not a single relation but an entire class of relations. The user above mentioned monoids. That is one very common composition that is omnipresent in computation and yet completely glossed over in most programming languages.

But there are other compositions. In particular, for something like process connection, the language of arrows or Cartesian categories is appropriate to model the choices. The actual implementation is another story

In general when you want to model something you first need to decide on the objects and then you need to decide on the relations between those objects. Inheritance is one and there's no need for it to be treated specially. You will find though that very objects actually fit any model of inheritance while many have obvious algebras that are more natural to use