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1. • CommentRowNumber1.
   • CommentAuthorUrs
   • CommentTimeNov 2nd 2021
   • (edited Nov 2nd 2021)
   • PermaLink
   Author: Urs
   Format: MarkdownItexIn checking for how to best link to this statement from within a proof, I realized that, apparently, there was no real statement recorded anywhere on the $n$Lab. So here a bare minimum, the bare statement with pointer to HTT, just so that I can link to it. <a href="https://ncatlab.org/nlab/revision/groupoid+objects+in+an+%28infinity%2C1%29-topos+are+effective/1">v1</a>, <a href="https://ncatlab.org/nlab/show/groupoid+objects+in+an+%28infinity%2C1%29-topos+are+effective">current</a>

   In checking for how to best link to this statement from within a proof, I realized that, apparently, there was no real statement recorded anywhere on the $n$Lab.

   So here a bare minimum, the bare statement with pointer to HTT, just so that I can link to it.

   v1, current

2. • CommentRowNumber2.
   • CommentAuthorUrs
   • CommentTimeNov 2nd 2021
   • PermaLink
   Author: Urs
   Format: MarkdownItex[ duplicate ] <a href="https://ncatlab.org/nlab/revision/groupoid+objects+in+an+%28%E2%88%9E%2C1%29-topos+are+effective/1">v1</a>, <a href="https://ncatlab.org/nlab/show/groupoid+objects+in+an+%28%E2%88%9E%2C1%29-topos+are+effective">current</a>

   [ duplicate ]

   v1, current

3. • CommentRowNumber3.
   • CommentAuthorHurkyl
   • CommentTimeNov 2nd 2021
   • (edited Nov 2nd 2021)
   • PermaLink
   Author: Hurkyl
   Format: MarkdownItexI added a statement of the corollary that the category of groupoids is equivalent to the category of effective epimorphisms, since I didn't notice a statement elsewhere. Maybe it would be better to put something stating that on the effective epimorphism page, since there isn't an "effective groupoid" page? <a href="https://ncatlab.org/nlab/revision/diff/groupoid+objects+in+an+%28%E2%88%9E%2C1%29-topos+are+effective/2">diff</a>, <a href="https://ncatlab.org/nlab/revision/groupoid+objects+in+an+%28%E2%88%9E%2C1%29-topos+are+effective/2">v2</a>, <a href="https://ncatlab.org/nlab/show/groupoid+objects+in+an+%28%E2%88%9E%2C1%29-topos+are+effective">current</a>

   I added a statement of the corollary that the category of groupoids is equivalent to the category of effective epimorphisms, since I didn’t notice a statement elsewhere.

   Maybe it would be better to put something stating that on the effective epimorphism page, since there isn’t an “effective groupoid” page?

   diff, v2, current

4. • CommentRowNumber4.
   • CommentAuthorUrs
   • CommentTimeNov 2nd 2021
   • PermaLink
   Author: Urs
   Format: MarkdownItexThanks. I have rephrased a little in order to display the actual equivalence of $\infty$-categories. Also added pointer to where in HTT this is discussed. Regarding your question: Not sure if I am reading it right but it sounds like you are asking if it would be good to further improve related entries. The answer to that is Yes, always. <a href="https://ncatlab.org/nlab/revision/diff/groupoid+objects+in+an+%28%E2%88%9E%2C1%29-topos+are+effective/3">diff</a>, <a href="https://ncatlab.org/nlab/revision/groupoid+objects+in+an+%28%E2%88%9E%2C1%29-topos+are+effective/3">v3</a>, <a href="https://ncatlab.org/nlab/show/groupoid+objects+in+an+%28%E2%88%9E%2C1%29-topos+are+effective">current</a>

   Thanks. I have rephrased a little in order to display the actual equivalence of $\infty$-categories. Also added pointer to where in HTT this is discussed.

   Regarding your question: Not sure if I am reading it right but it sounds like you are asking if it would be good to further improve related entries. The answer to that is Yes, always.

   diff, v3, current

5. • CommentRowNumber5.
   • CommentAuthorUrs
   • CommentTimeNov 2nd 2021
   • PermaLink
   Author: Urs
   Format: MarkdownItexadded the remark ([here](https://ncatlab.org/nlab/show/groupoid+objects+in+an+infinity1-topos+are+effective#InterpretationInTermsOfInfinityStacksWithAtlases)) how the theorem recovers the traditional relation between internal groupoids and geometric stacks equipped with atlases (following [p. 27](https://arxiv.org/pdf/2008.01101.pdf#page=27) in [[schreiber:Proper Orbifold Cohomology|SS20]]) <a href="https://ncatlab.org/nlab/revision/diff/groupoid+objects+in+an+%28%E2%88%9E%2C1%29-topos+are+effective/4">diff</a>, <a href="https://ncatlab.org/nlab/revision/groupoid+objects+in+an+%28%E2%88%9E%2C1%29-topos+are+effective/4">v4</a>, <a href="https://ncatlab.org/nlab/show/groupoid+objects+in+an+%28%E2%88%9E%2C1%29-topos+are+effective">current</a>

   added the remark (here) how the theorem recovers the traditional relation between internal groupoids and geometric stacks equipped with atlases (following p. 27 in SS20)

   diff, v4, current