The paper by Raptis and Strunk describes a model for motivic homotopy theory as a model topos. I wonder what this result can lead to or what is the possible development of the relation between motivic homotopy theory and infinity topos? Can anyone suggest an overview or some references please?

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notan $\infty$-topos. The contribution of Raptis and Strunk is to provide an alternative $\infty$-category whichisan $\infty$-topos and plausibly encodes similar information. As far as I know (though I am not an expert in this area) the promise of this construction has not been fully explored. Note that there are other $\infty$-toposes, such as the etale site, which are related to motivic homotopy theory less directly. $\endgroup$ – Tim Campion Jul 3 at 16:30