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Results tagged with infinity-topos-theory
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user 102343
5
votes
Accepted
Does every $\kappa$-compact topos embedd relatively $\kappa$-tidily into a presheaf topos?
The answer is no.
Counterexamples for $\kappa = \omega$ are given by sheaves on a compact topological space $X$, where $\Gamma(X,-)$ commutes with filtered colimits. However, the condition that you as …
- 15.8k
7
votes
Accepted
$\infty$-topos as an internal $\infty$-category in itself
In Martini and Wolf's series on internal higher category theory, they prove an equivalence between sheaves of categories on an $\infty$-topos $B$ and internal categories in $B$.
The former is better s …
- 15.8k
2
votes
Accepted
$\infty$-topoi versus condensed anima
So I think Dustin's comment and the linked comment thread answer most of the questions, if not all. I think it would nonetheless be good to have an account here so let me try to write a coherent answe …
- 15.8k
15
votes
Reflection principle vs universes
If I understand correctly, you're after a statement of the form :
"If something was proved in HTT using universes, it can be proved without them by restricting to some $V_\kappa$ for $\kappa$ large e …
- 15.8k