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Results tagged with sites
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user 22131
For questions related to the mathematical notion of site, which among others generalizes the notion of topological space. For questions on internet-sites, use online-resources, but note that these questions need to be very specific to research-level mathematics to be on-topic.
2
votes
Accepted
Stacks for the extensive topology?
This a genral fact: the coproducts in an extensive category are disjoint so the sheaf/stack condition with respect to a cover by the coproduct injection exactly say that the coproduct is sent to a pro …
- 42.4k
4
votes
Accepted
Necessary and sufficient conditions for all sheaves on a site to be continuous functors?
Given a category $C$, and a familly of co-cone in $C$ (you can take all colimit cocone in $C$ if you want - the family doesn't even have to be small) there is a smallest topology on $C$ so that sheave …
- 42.4k
16
votes
Why is $1$ not a dense sub-site in a group with the trivial Grothendieck topology?
To complement the answer by Peter, I think the "correct" statement of the comparison lemma for non-full subcategory (and in fact even non-faithful functor) can be found in a paper by (A.)Kock and Moer …
- 42.4k
13
votes
Accepted
Tensor product of sites
The category $H$ can be described as the category of $E$-valued sheaves on $D$, or $F$-valued sheaves on $C$.
You get a site by taking the category $C \times D$ and taking the topology generated by th …
- 42.4k
9
votes
Accepted
Relationship between canonical topology on a topos and its site of definition
This is essentially correct, and there is no need for the topology to be subcanonical. But let me clarify:
Whether the topology is subcaninical or not, we have the following: given any family of maps …
- 42.4k