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Background: If one works with sheaves on small etale site over a fixed scheme (which is really an essentially large category), one can instead work with sheaves on the affine etale site (which turns out to be an essentially small category) as their sheaves categories coincide. The consequence is that all etale sheaves are small in the sense that they are small colimits of some representables.

The above consideration doesn't seem to work for big sites. My question is : Are all the fppf sheaves small (in the above sense) in the big fppf site? If no, do we have a characterization of the small sheaves here?

Background: If one works with sheaves on small etale site over a fixed scheme (which is really an essentially large category), one can instead work with sheaves on the affine etale site (which turns out to be an essentially small category) as their sheaves categories coincide. The consequence is that all etale sheaves are small in the sense that they are small colimits of some representables.

The above consideration doesn't seem to work for big sites. My question is : Are all the fppf sheaves small (in the above sense i.e. small colimits of representables) in the big fppf site? If no, do we have a characterization of the small sheaves here?

Background: If one works with sheaves on small etale site over a fixed scheme (which is really an essentially large category), one can instead work with sheaves on the affine etale site (which turns out to be an essentially small category) as their sheaves categories coincide. The consequence is that all etale sheaves are small in the sense that they are colimits of the representables.

The above consideration doesn't seem to work for big sites. My question is : Are all the fppf sheaves small (in the above sense) in the big fppf site? If no, do we have a characterization of the small sheaves here?

Background: If one works with sheaves on small etale site over a fixed scheme (which is really an essentially large category), one can instead work with sheaves on the affine etale site (which turns out to be an essentially small category) as their sheaves categories coincide. The consequence is that all etale sheaves are small in the sense that they are small colimits of some representables.

The above consideration doesn't seem to work for big sites. My question is : Are all the fppf sheaves small (in the above sense) in the big fppf site? If no, do we have a characterization of the small sheaves here?