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Results tagged with infinity-topos-theory
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user 4528
6
votes
Accepted
Hypercovers of sheaves in classical and quasi-categories
Local epimorphisms are precisely those morphisms in $\mathcal{P}\left(\mathcal{C}\right)$ which become effective epimorphisms after applying the sheafification functor. In particular, if $f$ is an eff …
- 15.5k
5
votes
Is the site of (smooth) manifolds hypercomplete?
I think you can argue like this:
Let $l:Cart \to Mfd$ be the inclusion of the full subcategory of smooth manifolds consisting of the Euclidean ones ($\mathbb{R}^n$'s). It induces an essential geometr …
- 15.5k
4
votes
Accepted
Site dependance of the Cech weak equivalences on simplicial sheaves
It is independent, provided the two sites of definition, also yield the same infinity topos (so e.g. when they both have finite limits, or the infinity-topos is hypercomplete). Given two simplicial ob …
- 15.5k
4
votes
Canonical topology for infinity topoi revisited.
I will write what I think is a proof that in fact every infinity topos is equivalent to sheaves over itself. Please let me know if I am making any errors. I am basically adapting a proof from SGA4 of …
- 15.5k
2
votes
Canonical topology for infinity topoi revisited.
I've convinced myself the answer is the following CLAIM however, I have not finished proving it yet, but it is too long to leave as a comment. Hopefully soon I will update this with a proof of the cl …
- 15.5k