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For questions related to the mathematical notion of site, which among others generalizes the notion of topological space. For questions on internet-sites, use online-resources, but note that these questions need to be very specific to research-level mathematics to be on-topic.
5
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Examples of nonstable ∞-categories in which sifted colimits commute with finite limits
What are some natural examples (if any) of nonstable ∞-categories in which finite limits commute with sifted colimits (or rather just colimits over Δ^op)?
Stable ∞-categories do satisfy this property …
7
votes
0
answers
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What is a morphism of ∞-sites?
If both sites have finite limits, then covering-flat functors are precisely the functors that preserve finite limits.
What is the analogue of this story for ∞-sites? … What is a covering-flat functor between ∞-sites?
If both ∞-sites admit finite ∞-limits, then covering-flat functors could be defined
as finite ∞-limit preserving functors. …
7
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1
answer
343
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Which dense inclusions of sites are ∞-dense?
As it turns out, in the 1-categorical case we have an ample supply of dense inclusions of sites,
as explained by Proposition C2.2.16 of Johnstone's Sketches of an Elephant:
essentially small sites of definition … What additional conditions are needed to ensure that a dense inclusion of sites is ∞-dense? …