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I have added statement and proof (here) that for $\mathbf{H}$ cohesive and $X \in \mathbf{H}$, the shape of the slice $\mathbf{H}_{/X}$ is the cohesive shape of $X$.
(This seems to be the kind of statement we would/should have considered in the first wave of edits to this entry, but I don’t see or recall that we did.)
I have worked more on the Definition section (here):
split up the previous Prop about equivalence of definitions into an actual numbered definition followed by a proposition that two Defs are equivalent
added a third definition: as image of terminal object under the pro-left adjoint to $LConst$
added the argument how that is equivalent to the other definition.
added exact references to page and verse in the articles that have stated these definitions (this was at least unclear in the previous version).
The idea-section used to essentially just mention the idea of the shape of $Sh_\infty(X)$ for a topological space $X$, in relation to classical shape.
I have added (here)
two sentences to before this, in order to indicate the idea more generally and mentioning the relation to étale homotopy type,
a sentence after this, mentioning the relation to cohesive shape for slices of cohesive toposes.
I have merged the first two Examples-subsections (shape of locally $\infty$-connected and of “retracts”) into a single section, since both subsections were small while having considerable overlap.
Also turned the first remark there (from times back, that the shape is given by the left adjoint when it exists) into a numbered Proposition with a proof, and added the remark that this is a special case of the previous proposition on étale homotopy type.
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