Six model categories for directed homotopy

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.

25 pages, 3 figures

References in corpus (4)

• On the construction of functorial factorizations for model categories
• Lifting accessible model structures
• Flows revisited: the model category structure and its left determinedness
• Enriched diagrams of topological spaces over locally contractible enriched categories

Cited by in corpus (3)

• Homotopy theory of Moore flows (I)
• Homotopy theory of Moore flows (II)
• Comparing cubical and globular directed paths