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Results tagged with infinity-topos-theory
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user 51164
26
votes
1
answer
1k
views
Is the $\infty$-topos $Sh(X)$ hypercomplete whenever $X$ is a CW complex?
It can be shown (see Is every paracompact, Hausdorff, locally contractible space homotopy equivalent to a CW complex?) that if $X$ is a locally contractible paracompact Hausdorff space such that the $ …
- 9,491
5
votes
Accepted
A finite Whitehead Theorem for $\infty$-topos
Let $\mathcal{X}$ be the $\infty$-topos in question containing an object $X \in \mathcal{X}$. I assume that by $X$ having homotopy dimension $\leq n$ you mean that the $\infty$-topos $\mathcal{X}_{/X} …
- 9,491
7
votes
Accepted
What is a spectrum object in $\infty$-topoi?
Following up on the answer of Simon Henry, let us prove the following statement. For a pro-space $\hat{X} = \{X_i\}_{i \in I}$, we let $Spaces_{/\hat{X}}$ denote the $\infty$-topos defined as the (co …
- 9,491
3
votes
Accepted
Stability of accessible $\infty$-categories under some operations
For (2) I suggested a possible solution for this here: Lemma 5.4.5.11 of HTT.
For (3) it really appears to be a typo and can be fixed as in the comment of dhy. For (1), as explained by Tim in the comm …
- 9,491