nForum - Discussion Feed (Descent for categories of sheaves)2024-03-29T15:52:13+00:00https://nforum.ncatlab.org/
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Dmitri Pavlov comments on "Descent for categories of sheaves" (67009)https://nforum.ncatlab.org/discussion/8256/?Focus=67009#Comment_670092018-01-26T05:48:43+00:002024-03-29T15:52:13+00:00Dmitri Pavlovhttps://nforum.ncatlab.org/account/356/
Thanks! Somehow I missed item (3) when looking through section 6.1.3.
Thanks! Somehow I missed item (3) when looking through section 6.1.3.
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Marc Hoyois comments on "Descent for categories of sheaves" (66982)https://nforum.ncatlab.org/discussion/8256/?Focus=66982#Comment_669822018-01-23T15:22:13+00:002024-03-29T15:52:13+00:00Marc Hoyoishttps://nforum.ncatlab.org/account/409/
This is Theorem 6.1.3.9 (3) in HTT.
This is Theorem 6.1.3.9 (3) in HTT.
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JonasFrey comments on "Descent for categories of sheaves" (66976)https://nforum.ncatlab.org/discussion/8256/?Focus=66976#Comment_669762018-01-23T03:55:06+00:002024-03-29T15:52:13+00:00JonasFreyhttps://nforum.ncatlab.org/account/256/
I think a special case of this (for sheaves over spaces) is given as Exercise 2.7.D of Vakil’s Rising Sea. See also Remark 2.7.5.
I think a special case of this (for sheaves over spaces) is given as Exercise 2.7.D of Vakil’s Rising Sea. See also Remark 2.7.5.
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Dmitri Pavlov comments on "Descent for categories of sheaves" (66975)https://nforum.ncatlab.org/discussion/8256/?Focus=66975#Comment_669752018-01-23T01:02:45+00:002024-03-29T15:52:13+00:00Dmitri Pavlovhttps://nforum.ncatlab.org/account/356/
Fix some site S.Consider the presheaf Sh on S valued in the bicategory of categoriesthat sends s∈S to the category of sheaves over the slice site S/s.One can show that Sh is actually a sheaf of ...
Fix some site S. Consider the presheaf Sh on S valued in the bicategory of categories that sends s∈S to the category of sheaves over the slice site S/s. One can show that Sh is actually a sheaf of categories (or rather a stack in bicategories, to be precise).
In other words, a sheaf can be specified locally on the elements of some cover and then glued together, and the same is true for morphisms of sheaves.
Is this fact somewhere in the literature? I am also interested in the versions for ∞-sheaves on ∞-sites (any model will do).
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