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1. • CommentRowNumber1.
   • CommentAuthorMike Shulman
   • CommentTimeDec 25th 2009
   • PermaLink
   Author: Mike Shulman
   Format: MarkdownAdded comments to [[regular category]], [[exact category]], [[coherent category]], and [[pretopos]] about under precisely what conditions the [[codomain fibration]] is a stack for the relevant Grothendieck topology. Also added some thoughts about "pre-lextensive categories" to [[extensive category]].

   Added comments to regular category, exact category, coherent category, and pretopos about under precisely what conditions the codomain fibration is a stack for the relevant Grothendieck topology. Also added some thoughts about "pre-lextensive categories" to extensive category.

2. • CommentRowNumber2.
   • CommentAuthorUrs
   • CommentTimeDec 28th 2009
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   Author: Urs
   Format: MarkdownI used your remarks on topologies to create a subsection <a href="http://ncatlab.org/nlab/show/Grothendieck+topology#Examples">Examples</a> at [[Grothendieck topology]]

   I used your remarks on topologies to create a subsection Examples at Grothendieck topology

3. • CommentRowNumber3.
   • CommentAuthorUrs
   • CommentTimeApr 8th 2023
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   Author: Urs
   Format: MarkdownItexOver [here](https://nforum.ncatlab.org/discussion/16319/codomain-fibration-is-a-stackreference-request-want-a-proof/?Focus=108429#Comment_108429) is a reference request for the claims in the edits announced in [#1](#Comment_3483) above. Looking around, it appears that these edits were prompted by discussion at [MO:q/9636](https://mathoverflow.net/q/9636/381), where relevant details were spelled out in the last part of the reply by Anton Geraschenko: [MO:a/9663](https://mathoverflow.net/a/9663/381), who mainly pointed out the "descent for sheaves"-theorem, a proof of which is spelled out in: * [[Martin Olsson]], §4.2.11 of: *Algebraic Spaces and Stacks*, Colloquium Publications **62** (2016) [[doi:10.1090/coll/062](https://doi.org/10.1090/coll/062), [ISBN:978-1-4704-2798-6](https://bookstore.ams.org/coll-62)] These or other relevant pointers should be added to all those entries in [#1](#Comment_3483).

   Over here is a reference request for the claims in the edits announced in #1 above.

   Looking around, it appears that these edits were prompted by discussion at MO:q/9636, where relevant details were spelled out in the last part of the reply by Anton Geraschenko: MO:a/9663, who mainly pointed out the “descent for sheaves”-theorem, a proof of which is spelled out in:

   • Martin Olsson, §4.2.11 of: Algebraic Spaces and Stacks, Colloquium Publications 62 (2016) [doi:10.1090/coll/062, ISBN:978-1-4704-2798-6]

   These or other relevant pointers should be added to all those entries in #1.