Directed homotopy theory, II. Homotopy constructs

Directed Algebraic Topology studies phenomena where privileged directions appear, derived from the analysis of concurrency, traffic networks, space-time models, etc.This is the sequel of a paper, 'Directed homotopy theory, I.The fundamental category', where we introduced directed spaces, their non reversible homotopies and their fundamental category.Here we study some basic constructs of homotopy, like homotopy pushouts and pullbacks, mapping cones and homotopy fibres, suspensions and loops, cofibre and fibre sequences.