In proposition 2.7. of the condensed notes of professors Scholze and Clausen it is said that the category of extremally disconnected sets is a site, but in the definition of a site in the Stacks Project (<https://stacks.math.columbia.edu/tag/00VH>) it is necessary for a site to have fibre products sometimes (Axiom (3) in the definition) and extremally disconnected sets don't have all fibre products.


The category of extremally disconnected sets is a site using the definition from the Stacks Project?



The site of extremally disconnected sets
Usage varies. Let's at least stipulate that "site" is synonymous with "category equipped with a Grothendieck topology".


Some, but not all, authors, require a site to have pullbacks, because this assumption simplifies the definition a bit. But e.g. the [nlab](https://nlab-pages.s3.us-east-2.amazonaws.com/nlab/show/Grothendieck+topology#definition_using_sieves) gives the definition which doesn't assume one has pullbacks. Apparently this version of the definition goes back at least to SGA 4.


