At some point I had made up the extra axiom/terminology saying that an object $\mathbb{A}^1$ in a cohesive $\infty$-topos “exhibits the cohesion” if the shape modality is equivalent to $\mathbb{A}^1$-localization. Now I was talking about that assumption with Mike and noticed that this didn’t have a reflection on the $n$Lab yet.

So now I have added, for the record, the definition here at “cohesive oo-topos” and cross-linked with the existing discussion at “continuum”.

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