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1. • CommentRowNumber1.
   • CommentAuthorDmitri Pavlov
   • CommentTime3 days ago
   • PermaLink
   Author: Dmitri Pavlov
   Format: MarkdownItexFixed a hyperlink to Jardine's lectures. Removed a query box: +-- {: .query} Can any of you size-issue experts help to clarify this? _Mike_: I wish. I added some stuff, but I still don't really understand this business. In particular I don't really know what is meant by "inessential." It certainly seems unlikely that you would get _equivalent_ homotopy theories, but it does seem likely that you would get similar behavior no matter where you draw the line. And if all you care about is, say, having a good category of sheaves in which you can embed any _particular_ space or manifold you happen to care about, then that may be good enough. But I don't really know what the goal is of considering such large sites. =-- <a href="https://ncatlab.org/nlab/revision/diff/large+site/9">diff</a>, <a href="https://ncatlab.org/nlab/revision/large+site/9">v9</a>, <a href="https://ncatlab.org/nlab/show/large+site">current</a>

   Fixed a hyperlink to Jardine’s lectures. Removed a query box:

   +– {: .query} Can any of you size-issue experts help to clarify this?

   Mike: I wish. I added some stuff, but I still don’t really understand this business. In particular I don’t really know what is meant by “inessential.” It certainly seems unlikely that you would get equivalent homotopy theories, but it does seem likely that you would get similar behavior no matter where you draw the line. And if all you care about is, say, having a good category of sheaves in which you can embed any particular space or manifold you happen to care about, then that may be good enough. But I don’t really know what the goal is of considering such large sites. =–

   diff, v9, current