Mathematically, branes can be described using the notion of a category. This is a mathematical structure consisting of "objects", and for any pair of objects, a set of "morphisms" between them. In most examples, the objects are mathematical structures (such as sets, vector spaces, or topological spaces) and the morphisms are functions between these structures. One can also consider categories where the objects are D-branes and the morphisms between two branes formula_3 and formula_4 are states of open strings stretched between formula_3 and formula_4.