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1. • CommentRowNumber1.
   • CommentAuthornLab edit announcer
   • CommentTimeMay 8th 2022
   • PermaLink
   Author: nLab edit announcer
   Format: MarkdownItexPage created, but author did not leave any comments. Anonymous <a href="https://ncatlab.org/nlab/revision/sigma-pretopos/1">v1</a>, <a href="https://ncatlab.org/nlab/show/sigma-pretopos">current</a>

   Page created, but author did not leave any comments.

   Anonymous

   v1, current

2. • CommentRowNumber2.
   • CommentAuthorUrs
   • CommentTimeMay 8th 2022
   • (edited May 8th 2022)
   • PermaLink
   Author: Urs
   Format: MarkdownItexhave replaced "The groupoidification of a ..." by "A [[categorification]] of the notion of ... " added the floating context menu "Topos Theory" hyperlinked *[[Sketches of an Elephant]]* maybe one could be more specific about where in the two volumes cited the reader should go hunt for $\sigma$-pretopoi <a href="https://ncatlab.org/nlab/revision/diff/sigma-pretopos/2">diff</a>, <a href="https://ncatlab.org/nlab/revision/sigma-pretopos/2">v2</a>, <a href="https://ncatlab.org/nlab/show/sigma-pretopos">current</a>

   have replaced “The groupoidification of a …” by “A categorification of the notion of … “

   added the floating context menu “Topos Theory”

   hyperlinked Sketches of an Elephant

   maybe one could be more specific about where in the two volumes cited the reader should go hunt for $\sigma$-pretopoi

   diff, v2, current

3. • CommentRowNumber3.
   • CommentAuthorDavidRoberts
   • CommentTimeMay 9th 2022
   • PermaLink
   Author: DavidRoberts
   Format: MarkdownItexAdded examples: >* Any [[https://ncatlab.org/nlab/show/pretopos#infinitary|infinitary pretopos]] is a $\sigma$-topos. >* The category of countable sets (for instance, subquotients of the natural numbers $\mathbb{N}$) is a $\sigma$-pretopos. and a pointer to a specific section inside part A of The Elephant to the concept, where the references just cited the whole book (both parts). <a href="https://ncatlab.org/nlab/revision/diff/sigma-pretopos/3">diff</a>, <a href="https://ncatlab.org/nlab/revision/sigma-pretopos/3">v3</a>, <a href="https://ncatlab.org/nlab/show/sigma-pretopos">current</a>

   Added examples:

   • Any infinitary pretopos is a $\sigma$-topos.

   • The category of countable sets (for instance, subquotients of the natural numbers $\mathbb{N}$) is a $\sigma$-pretopos.

   and a pointer to a specific section inside part A of The Elephant to the concept, where the references just cited the whole book (both parts).

   diff, v3, current

4. • CommentRowNumber4.
   • CommentAuthorDavidRoberts
   • CommentTimeMay 10th 2022
   • PermaLink
   Author: DavidRoberts
   Format: MarkdownItexAdded another example and a reference for it. <a href="https://ncatlab.org/nlab/revision/diff/sigma-pretopos/4">diff</a>, <a href="https://ncatlab.org/nlab/revision/sigma-pretopos/4">v4</a>, <a href="https://ncatlab.org/nlab/show/sigma-pretopos">current</a>

   Added another example and a reference for it.

   diff, v4, current

5. • CommentRowNumber5.
   • CommentAuthorDavidRoberts
   • CommentTimeMay 10th 2022
   • PermaLink
   Author: DavidRoberts
   Format: MarkdownItexAdded reference to work of Zhen Lin Low doing simplicial homotopy theory internal to a $\sigma$-pretopos <a href="https://ncatlab.org/nlab/revision/diff/sigma-pretopos/4">diff</a>, <a href="https://ncatlab.org/nlab/revision/sigma-pretopos/4">v4</a>, <a href="https://ncatlab.org/nlab/show/sigma-pretopos">current</a>

   Added reference to work of Zhen Lin Low doing simplicial homotopy theory internal to a $\sigma$-pretopos

   diff, v4, current

6. • CommentRowNumber6.
   • CommentAuthorUrs
   • CommentTimeMay 10th 2022
   • PermaLink
   Author: Urs
   Format: MarkdownItexI have added hyperlinks to *[[Zhen Lin Low]]*, *[[effective quotient|effective]]*, *[[subquotient]]*, *[[contable set]]* and more. <a href="https://ncatlab.org/nlab/revision/diff/sigma-pretopos/5">diff</a>, <a href="https://ncatlab.org/nlab/revision/sigma-pretopos/5">v5</a>, <a href="https://ncatlab.org/nlab/show/sigma-pretopos">current</a>

   I have added hyperlinks to Zhen Lin Low, effective, subquotient, contable set and more.

   diff, v5, current

7. • CommentRowNumber7.
   • CommentAuthorDavidRoberts
   • CommentTimeMay 10th 2022
   • PermaLink
   Author: DavidRoberts
   Format: MarkdownItexThanks, was being a bit brief and hasty.

   Thanks, was being a bit brief and hasty.

8. • CommentRowNumber8.
   • CommentAuthorDavidRoberts
   • CommentTimeMay 10th 2022
   • PermaLink
   Author: DavidRoberts
   Format: MarkdownItexActually, I'm not sure I agree that the Giraud-esque definition should include the condition of having a generating set. The notion works perfectly fine as an elementary definition, and we don't demand that a pretopos has a generating set. One could add this condition to get a concept midway between a Grothendieck topos (an infinitary pretopos with a generating set) and a general pretopos: having _some_ infinite colimits, but not all.

   Actually, I’m not sure I agree that the Giraud-esque definition should include the condition of having a generating set. The notion works perfectly fine as an elementary definition, and we don’t demand that a pretopos has a generating set. One could add this condition to get a concept midway between a Grothendieck topos (an infinitary pretopos with a generating set) and a general pretopos: having some infinite colimits, but not all.

9. • CommentRowNumber9.
   • CommentAuthorDavidRoberts
   • CommentTimeMay 10th 2022
   • PermaLink
   Author: DavidRoberts
   Format: MarkdownItexAdded 'see also' to [[geometric category]], which generalises to other sizes of possible colimits. <a href="https://ncatlab.org/nlab/revision/diff/sigma-pretopos/6">diff</a>, <a href="https://ncatlab.org/nlab/revision/sigma-pretopos/6">v6</a>, <a href="https://ncatlab.org/nlab/show/sigma-pretopos">current</a>

   Added ’see also’ to geometric category, which generalises to other sizes of possible colimits.

   diff, v6, current