4 problems

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Left properness conjecture for q-model structures on multipointed d-spaces
Take ${\mathbf{Top}}$ to be the category of $\Delta$ -Hausdorff $\Delta$ -generated spaces. Left properness conjecture. The q-model structures of ${\rm{\mathbf{{\mathcal{G}}dTop}}}$ …
Conjectureopendirected-topology homotopy-theory model-categoriesarXiv posted 2 days ago
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H-cofibrancy conjecture for regular directed realizations of precubical sets
Let $K$ be a precubical set, and let $|K|^t_{reg}$ denote its regular multipointed $d$ -space realization. A multipointed $d$ -space is called h-cofibrant when it is cofibrant in the…
Conjectureopendirected-topology homotopy-theoryarXiv posted 2 days ago
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The $k$ -connected past-link conjecture for directed path spaces
Past-link connectivity conjecture. Similar results for $k$ -connected past links should follow from the $k$ -connected Nerve Lemma.
Conjectureopendirected-topology higher-connectivity nerve-lemmaarXiv posted 2 days ago
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The directed topological complexity conjecture for NPC cubical complexes
Directed topological complexity conjecture. We conjecture that
Conjectureopendirected-topology event-structures topological-complexityarXiv posted 2 days ago

Left properness conjecture for q-model structures on multipointed d-spaces