  Globular complexes were introduced by E. Goubault and the author in
arXiv:math/0107060 to model higher dimensional automata. Globular complexes are
topological spaces equipped with a globular decomposition which is the directed
analogue of the cellular decomposition of a CW-complex. We prove that there
exists a combinatorial model category such that the cellular objects are
exactly the globular complexes and such that the homotopy category is
equivalent to the homotopy category of flows introduced in arXiv:math/0308054.
The underlying category of this model category is a variant of M. Grandis'
notion of d-space over a topological space colimit generated by simplices. This
result enables us to understand the relationship between the framework of flows
and other works in directed algebraic topology using d-spaces. It also enables
us to prove that the underlying homotopy type functor of flows constructed in
arXiv:math/0308063 can be interpreted up to equivalences of categories as the
total left derived functor of a left Quillen adjoint.
