%0 Journal Article
%T Six model categories for directed homotopy
%J Categories and General Algebraic Structures with Applications
%I Shahid Beheshti University
%Z 2345-5853
%A Gaucher, Philippe
%D 2021
%\ 07/01/2021
%V 15
%N 1
%P 145-181
%! Six model categories for directed homotopy
%K d-space
%K flow
%K topological model of concurrency
%K combinatorial model category
%K accessible model category
%K locally presentable category
%K enriched semicategory
%K enriched non-unital category
%R 10.52547/cgasa.15.1.145
%X We 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.
%U https://cgasa.sbu.ac.ir/article_101064_54e15c5a207051449a58ecc86c267e56.pdf