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Karol Szumiło's user avatar
Karol Szumiło's user avatar
Karol Szumiło's user avatar
Karol Szumiło
  • Member for 13 years, 10 months
  • Last seen more than 1 year ago
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Are cofibrations accessible?
Take a look at Lemma 2.11 in arxiv.org/abs/1802.09889. This doesn't answer your question, but is relevant.
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Bisimplicial sets and homology
Oh yes, I don't have a counterexample in mind, but I would be very surprised if this worked for surjections or injections.
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Homotopy limits of Simplicial sets
@SimonHenry This is not true for all Reedy categories, only for those with "cofibrant constants" and $\Delta$ happens not to be one. (See ncatlab.org/nlab/show/Reedy+category+with+fibrant+constants)
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(Co)limits of locally cartesian closed categories
If you don't include terminal objects, then I agree that coproducts and filtered colimits are preserved. I don't believe this is the case for pushouts though.
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