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1. • CommentRowNumber1.
   • CommentAuthornLab edit announcer
   • CommentTimeOct 24th 2024
   • PermaLink
   Author: nLab edit announcer
   Format: MarkdownItexstarting page on $\mathbb{Z}$-functors Anonymouse <a href="https://ncatlab.org/nlab/revision/Z-functor/1">v1</a>, <a href="https://ncatlab.org/nlab/show/Z-functor">current</a>

   starting page on $\mathbb{Z}$-functors

   Anonymouse

   v1, current

2. • CommentRowNumber2.
   • CommentAuthorzskoda
   • CommentTimeOct 25th 2024
   • PermaLink
   Author: zskoda
   Format: MarkdownItexIt seems, some obscure terminology.

   It seems, some obscure terminology.

3. • CommentRowNumber3.
   • CommentAuthorUrs
   • CommentTimeOct 27th 2024
   • (edited Oct 27th 2024)
   • PermaLink
   Author: Urs
   Format: MarkdownItexYeah, it's not particularly convincing terminology. Also, it clashes with the terminology of *[[Z-categories]]*.

   Yeah, it’s not particularly convincing terminology. Also, it clashes with the terminology of Z-categories.

4. • CommentRowNumber4.
   • CommentAuthorDavidRoberts
   • CommentTimeOct 27th 2024
   • PermaLink
   Author: DavidRoberts
   Format: MarkdownItexMoreover, one wonders whether small (pre)sheaves, rather than all presheaves, might give the better concept, without running into size issues.

   Moreover, one wonders whether small (pre)sheaves, rather than all presheaves, might give the better concept, without running into size issues.

5. • CommentRowNumber5.
   • CommentAuthorzskoda
   • CommentTimeOct 28th 2024
   • PermaLink
   Author: zskoda
   Format: MarkdownItexI had a vague memory of this and I checked now, the terminology originates from Demazure-Gabriel famous functorial treatise on algebraic geometry and algebraic groups. They work with universes so the smallness is accounted for appropriately.

   I had a vague memory of this and I checked now, the terminology originates from Demazure-Gabriel famous functorial treatise on algebraic geometry and algebraic groups. They work with universes so the smallness is accounted for appropriately.

6. • CommentRowNumber6.
   • CommentAuthorDavidRoberts
   • CommentTimeOct 28th 2024
   • PermaLink
   Author: DavidRoberts
   Format: MarkdownItexI meant small in the sense of being a small colimit of representables, not valued in small sets, in case that wasn't clear. I see from [this MathOverflow answer](https://mathoverflow.net/a/121091/4177) D&G are imposing the constraint that a Z-functor is only defined on a subcategory of "very small" rings, relative to the smaller of a pair of universes.

   I meant small in the sense of being a small colimit of representables, not valued in small sets, in case that wasn’t clear. I see from this MathOverflow answer D&G are imposing the constraint that a Z-functor is only defined on a subcategory of “very small” rings, relative to the smaller of a pair of universes.

7. • CommentRowNumber7.
   • CommentAuthorUrs
   • CommentTimeOct 29th 2024
   • PermaLink
   Author: Urs
   Format: MarkdownItexSo I have added pointer to Demazure & Gabriel, and at the top a disambiguation warning regarding functors between Z-categories. <a href="https://ncatlab.org/nlab/revision/diff/Z-functor/3">diff</a>, <a href="https://ncatlab.org/nlab/revision/Z-functor/3">v3</a>, <a href="https://ncatlab.org/nlab/show/Z-functor">current</a>

   So I have added pointer to Demazure & Gabriel, and at the top a disambiguation warning regarding functors between Z-categories.

   diff, v3, current

8. • CommentRowNumber8.
   • CommentAuthorzskoda
   • CommentTimeOct 29th 2024
   • PermaLink
   Author: zskoda
   Format: MarkdownItex6 Oh, right, I forgot about that.

   6 Oh, right, I forgot about that.