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1. • CommentRowNumber1.
   • CommentAuthorDavidRoberts
   • CommentTimeDec 2nd 2010
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   Author: DavidRoberts
   Format: MarkdownItexApologies for the slew of paper related questions, but this one was bugging me too. Given a pretopology, or more generally, a coverage $J$ on a category, and the class of arrows ($J$-epi) of arrows that admit local sections relative to $J$. This class is interesting, but I'm interested in the subclass of arrows of which all pullbacks exist and which is stable under pullback (hence forms another pretopology). I denoted this $J_{sing}$ in my paper, because it is, if you like, the singletonification of $J$. This is clearly a Bad Name (TM), but I can't think of a good name. 'The class of pullback-stable $J$-epimorphisms' is also too much of a mouthful. It's a sort of saturation of $J$, but isn't saturated as I define the notion (and I have good reason to keep the definition of saturation as is). Any ideas?

   Apologies for the slew of paper related questions, but this one was bugging me too.

   Given a pretopology, or more generally, a coverage on a category, and the class of arrows (-epi) of arrows that admit local sections relative to . This class is interesting, but I’m interested in the subclass of arrows of which all pullbacks exist and which is stable under pullback (hence forms another pretopology). I denoted this in my paper, because it is, if you like, the singletonification of . This is clearly a Bad Name (TM), but I can’t think of a good name. ’The class of pullback-stable -epimorphisms’ is also too much of a mouthful. It’s a sort of saturation of , but isn’t saturated as I define the notion (and I have good reason to keep the definition of saturation as is).

   Any ideas?

2. • CommentRowNumber2.
   • CommentAuthorMike Shulman
   • CommentTimeDec 2nd 2010
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   Author: Mike Shulman
   Format: MarkdownItex"universally J-epic"? (To go along with "universally effective-epimorphic.")

   “universally J-epic”? (To go along with “universally effective-epimorphic.”)

3. • CommentRowNumber3.
   • CommentAuthorDavidRoberts
   • CommentTimeDec 2nd 2010
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   Author: DavidRoberts
   Format: MarkdownItexlet me try it: >"Let $J_u$ be the class of universally $J$-epi maps." (where now $J_{sing} \mapsto J_u$) Hmm. Then there is a nice double meaning to the ${}_u$, as it is an abbreviation of un. How about $J_{un}$? Is it too much of a pun?

   let me try it:

   “Let be the class of universally -epi maps.”

   (where now ) Hmm. Then there is a nice double meaning to the , as it is an abbreviation of un. How about ? Is it too much of a pun?

4. • CommentRowNumber4.
   • CommentAuthorTobyBartels
   • CommentTimeDec 3rd 2010
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   Author: TobyBartels
   Format: MarkdownItexWhat's the pun? Is it French? (I still don't see the pun.) By the way, I have seen "arrows of which all pullbacks exist" called "carrable", which seems to be the same French word showing up on [[quadrability|this nLab page]] (although not with quite the same meaning).

   What’s the pun? Is it French? (I still don’t see the pun.)

   By the way, I have seen “arrows of which all pullbacks exist” called “carrable”, which seems to be the same French word showing up on this nLab page (although not with quite the same meaning).

5. • CommentRowNumber5.
   • CommentAuthorDavidRoberts
   • CommentTimeDec 4th 2010
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   Author: DavidRoberts
   Format: MarkdownItex$un$ as in universal, and also as a singleton pretopology (of course, un = one). I'll go with $J_{un}$ I think.

   as in universal, and also as a singleton pretopology (of course, un = one). I’ll go with I think.

6. • CommentRowNumber6.
   • CommentAuthorTobyBartels
   • CommentTimeDec 4th 2010
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   Author: TobyBartels
   Format: MarkdownItexYes, of course, I forgot the meaning behind the original symbol! I also like the Anglo-French pun [$\mathbb{F}_{un}$](http://arxiv.org/abs/0909.2522).

   Yes, of course, I forgot the meaning behind the original symbol!

   I also like the Anglo-French pun .