The topology of critical processes, III (Computing homotopy)

Directed Algebraic Topology studies spaces equipped with a form of direction, to include models of non-reversible processes. In the present extension we also want to cover critical processes, indecomposable and unstoppable. The previous parts of this series introduced controlled spaces and their fundamental category. Here we study how to compute the latter. The homotopy structure of these spaces will be examined in Part IV.