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1. • CommentRowNumber1.
   • CommentAuthorMike Shulman
   • CommentTimeJan 6th 2011
   • (edited Jan 6th 2011)
   • PermaLink
   Author: Mike Shulman
   Format: MarkdownItexIs there a particular reason why the page [[Grothendieck topology]] uses a (what seems to me to be) nonstandard version of the definition in terms of sieves? The ones used at [[(∞,1)-site]] and [[2-site]], with three conditions (maximal sieves, pullback sieves, pullbacks cover implies a sieve covers), are in my experience the most common definition, but the page [[Grothendieck topology]] gives four conditions.

   Is there a particular reason why the page Grothendieck topology uses a (what seems to me to be) nonstandard version of the definition in terms of sieves? The ones used at (∞,1)-site and 2-site, with three conditions (maximal sieves, pullback sieves, pullbacks cover implies a sieve covers), are in my experience the most common definition, but the page Grothendieck topology gives four conditions.