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I made the following obvious fact more manifest in the respective $n$Lab entries:
a pregeometry (for structured (infinity,1)-toposes) $\mathcal{T}$ is a special case of a (multi-sorted) (infinity,1)-algbraic theory.
A structure $\infty$-sheaf
$\mathcal{O} : \mathcal{T} \to \mathcal{X}$on $\mathcal{X}$ is an $\infty$-algebra over this $\infty$-algebraic theory in $\mathcal{X}$. The extra conditions on it ensure that it indeed looks like a sheaf of function algebras .
(I added a respective remark to the discussion of pre-geometries and added an Example-sectoin with this to the entry of oo-alghebraic theories.)
The link should be to (infinity,1)-algebraic theory.
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