Not signed in (Sign In)

# Start a new discussion

## Not signed in

Want to take part in these discussions? Sign in if you have an account, or apply for one below

• Sign in using OpenID

## Site Tag Cloud

Vanilla 1.1.10 is a product of Lussumo. More Information: Documentation, Community Support.

• CommentRowNumber1.
• CommentAuthorUrs
• CommentTimeJan 6th 2011

created strongly infinity-connected site with the analogous definition, analogous proposition and analogous proof as at strongly connected site.

Only difference is that I define it as a cosifted $\infty$-connected site instead of as a cosifted locally $\infty$-connected site, because I am currently not quite sure about the definition of the latter because my model-category theoretic proofs rely on the existence of a terminal object, without that my standard Quillen adjunction model for the terminal $\infty$-geometric morphism fails and I’d need to think harder.

But all these entries of higher connected and local sites currently have the issue that they give sufficient conditions and don’t prove necessary conditions, so I think it’s okay, but we should keep in mind that there might be refinements of these definitions.

• CommentRowNumber2.
• CommentAuthorMike Shulman
• CommentTimeJan 6th 2011

Quick general comment: based on what I remember from the Elephant, in general the “necessary” condition will probably be of the form “if a topos has X property, then there exists a site with Y property which defines that topos.” Since all sorts of wacky sites can define the same topos, it seems unlikely one could find a condition on a particular site which is equivalent to its topos of sheaves having some property. Maybe that is obvious, but I thought I would recall it.

• CommentRowNumber3.
• CommentAuthorUrs
• CommentTimeJan 6th 2011

Right, okay I’ll think about it more.

Add your comments
• Please log in or leave your comment as a "guest post". If commenting as a "guest", please include your name in the message as a courtesy. Note: only certain categories allow guest posts.
• To produce a hyperlink to an nLab entry, simply put double square brackets around its name, e.g. [[category]]. To use (La)TeX mathematics in your post, make sure Markdown+Itex is selected below and put your mathematics between dollar signs as usual. Only a subset of the usual TeX math commands are accepted: see here for a list.

• (Help)