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arXiv · 1904.04159

Six model categories for directed homotopy

Philippe Gaucher
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Abstract

We construct a q-model structure, a h-model structure and a m-model structure on multipointed $d$-spaces and on flows. The two q-model structures are combinatorial and 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.

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Philippe Gaucher. 2019-04-08. Six model categories for directed homotopy. https://doi.org/10.52547/cgasa.15.1.145

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