Homotopy theory of Moore flows (III)

Le résumé fourni par la source

The previous paper of this series shows that the q-model categories of $\mathcal{G}$-multipointed $d$-spaces and of $\mathcal{G}$-flows are Quillen equivalent. In this paper, the same result is established by replacing the reparametrization category $\mathcal{G}$ by the reparametrization category $\mathcal{M}$. Unlike the case of $\mathcal{G}$, the execution paths of a cellular $\mathcal{M}$-multipointed $d$-space can have stop intervals. The technical tool to overcome this obstacle is the notion of globular naturalization. It is the globular analogue of Raussen's naturalization of a directed path in the geometric realization of a precubical set. The notion of globular naturalization working both for $\mathcal{G}$ and $\mathcal{M}$, the proof of the Quillen equivalence we obtain is valid for the two reparametrization categories. Together with the results of the first paper of this series, we then deduce that $\mathcal{G}$-multipointed $d$-spaces and $\mathcal{M}$-multipointed $d$-spaces have Quillen equivalent q-model structures. Finally, we prove that the saturation hypothesis can be added without any modification in the main theorems of the paper.

Ce résumé expose les affirmations des auteurs. BNTIC ne l’interprète pas comme une validation indépendante des résultats.