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Results tagged with infinity-topos-theory
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user 26470
10
votes
2
answers
857
views
Left Kan extension along Yoneda of pullback-preserving functor preserving pullbacks
Let $F\colon C \to D$ be a functor. The Kan Extension of $y_D \circ F$ along $y_C$ yields a functor $F_!: Fun(C^{op},Set) \to Fun(D^{op},Set)$. Here, $y_C$ and $y_D$ denotes the respective Yoneda embe …
5
votes
2
answers
756
views
Is an ∞-topos of local homotopy dimension $\leq n$ of homotopy dimension $\leq n$?
[All references are wrt to Lurie's "Higher Topos Theory" in its latest online available version (March 10, 2012)]
Definition 7.2.1.8:
An ∞-topos $X$ is locally of homotopy dimension $\leq n$ if there …
17
votes
2
answers
1k
views
Is the site of (smooth) manifolds hypercomplete?
By site of manifolds Man, I mean the category of manifolds (maybe submanifolds to obtain a small category) with continuous maps between them. A Grothendieck topology is given by open covers. Actually, …