Shahid Beheshti UniversityCategories and General Algebraic Structures with Applications2345-585315120210701Six model categories for directed homotopy14518110106410.52547/cgasa.15.1.145ENPhilippe GaucherUniversit\'e de Paris, CNRS, IRIF, F-75006, Paris, France.Journal Article20200120We construct a q-model structure, an h-model structure and an m-model structure on multipointed $d$-spaces and on flows. The two q-model structures are combinatorial and left determined and they coincide with the combinatorial model structures already known on these categories. The four other model structures (the two m-model structures and the two h-model structures) are accessible. We give an example of multipointed $d$-space and of flow which are not cofibrant in any of the model structures. We explain why the m-model structures, Quillen equivalent to the q-model structure of the same category, are better behaved than the q-model structures.https://cgasa.sbu.ac.ir/article_101064_54e15c5a207051449a58ecc86c267e56.pdf