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1. • CommentRowNumber1.
   • CommentAuthorUrs
   • CommentTimeNov 6th 2010
   • (edited Nov 6th 2010)
   • PermaLink
   Author: Urs
   Format: MarkdownItexI made the following obvious fact more manifest in the respective $n$Lab entries: a pre[[geometry (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.)

   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.)

2. • CommentRowNumber2.
   • CommentAuthorzskoda
   • CommentTimeNov 7th 2010
   • PermaLink
   Author: zskoda
   Format: MarkdownItexThe link should be to [[(infinity,1)-algebraic theory]].

   The link should be to (infinity,1)-algebraic theory.