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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} …
Yonatan Harpaz's user avatar
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 …
Yonatan Harpaz's user avatar
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 …
Yonatan Harpaz's user avatar