All Questions
Tagged with sheaf-theory sites
10 questions with no upvoted or accepted answers
13
votes
0
answers
481
views
Making the conceptual leap from locales to Grothendieck topologies?
I find the definition for locales and sheaves on locales to be straightforward, but I'm stumbling over the idea of a Grothendieck topology. Is there a nice way to see roughly how the latter ...
- 373
10
votes
0
answers
762
views
Differential Forms in Infinite Dimensions
In Kriegl/Michor's book "The convenient setting of global analysis", they define the space of differential $k$-forms on a possibly infinite-dimensional manifold $M$ as the space of smooth sections of ...
- 9,853
9
votes
0
answers
308
views
Refinement of hypercovers by ordinary covers
I am asking for references and discussions of statements of the form
Every bounded hypercover can be refined by an ordinary cover
By "bounded" I mean "finite height". E.g., are ...
- 4,519
7
votes
0
answers
362
views
What is a morphism of ∞-sites?
Recall that a morphism of sites
is a covering-flat functor
that preserves covering families.
Morphisms of sites can be identified with those
geometric morphisms of induced toposes
for which the ...
- 37.8k
6
votes
0
answers
183
views
Dense (∞,1)-subsites
So if $C$ is a 1-site and $D$ is a subsite (with the induced coverage), there are some conditions that ensure that the pre-composition and right Kan extension functors yield an equivalence of ...
- 439
5
votes
0
answers
448
views
Examples of nonstable ∞-categories in which sifted colimits commute with finite limits
What are some natural examples (if any) of nonstable ∞-categories in which finite limits commute with sifted colimits (or rather just colimits over Δ^op)?
Stable ∞-categories do satisfy this property,...
- 37.8k
3
votes
0
answers
530
views
Flasque sheaves on a site
This is a cross-post from MathStackexchange.
We define a flasque sheaf on a site as one whose first Čech cohomology vanishes for every covering of every object of the site. I know this definition is ...
- 153
2
votes
0
answers
296
views
Small sheaves on big sites
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 ...
- 319
2
votes
0
answers
264
views
Pullback of a constant sheaf over arbitrary sites
Given a geometric morphism between arbitrary Grothendieck topoi, $f:\mathcal{Sh(D)}\to\mathcal{Sh(C)}$, does the pullback $f^{-1}$ (i.e, the left adjoint) take constant sheafs to constant sheafs?
- 187
1
vote
0
answers
73
views
Why can we not convert GATs / EATs / limit sketches to sites?
I think I'm in the process of understanding something very subtle here, and I could use an expert's double check. So basically, my question is whether what I write is correct.
(Non-finitary) GATs, ...
- 511