A Homotopy Theory of Object-oriented Programming (DRAFT)

Abstract In object-oriented programming, the notion of a class (or typed data structure with bound behaviors) can be defined as a topological space and interpreted as a presheaf. We can then form higher categories for these classes and develop a homotopy theory to model their interactions. Interfaces provide programmatic invariances that may be treated at homotopy equivalences between implementing classes. One finds that object-oriented programming is a manifestation of a homotopy theory of higher categories.