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user 11640
10
votes
Grothendieck Topologies versus Pretopologies
A Grothendieck topology by definition consists of sieves – what Johnstone calls a sifted coverage – whereas a Grothendieck pretopology in any non-trivial case will contain a non-sieve. (Recall that $\ …
- 15.9k
17
votes
Accepted
Definition of ind-schemes
There is in fact no difference between the two definitions if you take your site to be the category of affine schemes – while it is true that the forgetful functor from sheaves to presheaves does not preserve …
- 15.9k