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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 votes
0 answers
428 views

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 …
Dmitri Pavlov's user avatar
7 votes
0 answers
359 views

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. …
Dmitri Pavlov's user avatar
7 votes
1 answer
343 views

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? …
Dmitri Pavlov's user avatar