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1. • CommentRowNumber1.
   • CommentAuthorUrs
   • CommentTimeJan 5th 2013
   • (edited Jan 5th 2013)
   • PermaLink
   Author: Urs
   Format: MarkdownItexcreated little entries * [[reduction modality]] $\dashv$ [[infinitesimal shape modality]] $\dashv$ [[infinitesimal flat modality]] to go along with the previous entries * [[shape modality]] $\dashv$ [[flat modality]] $\dashv$ [[sharp modality]] (whose $n$Forum-discussion is [here](http://nforum.mathforge.org/discussion/4594/shape-modality-flat-modality-sharp-modality/?Focus=37449#Comment_37449)) All of this is part of the [[cohesion - table]].

   created little entries

   • reduction modality $\dashv$ infinitesimal shape modality $\dashv$ infinitesimal flat modality

   to go along with the previous entries

   • shape modality $\dashv$ flat modality $\dashv$ sharp modality

   (whose $n$Forum-discussion is here)

   All of this is part of the cohesion - table.

2. • CommentRowNumber2.
   • CommentAuthorDavid_Corfield
   • CommentTimeJan 7th 2013
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   Author: David_Corfield
   Format: MarkdownItexSo whenever we come across a $\mathbf{\Pi}$, we should replace it by ʃ, right? E.g., many in this [section](http://ncatlab.org/nlab/show/cohesive+%28infinity%2C1%29-topos+--+infinitesimal+cohesion#StructuresInDifferentialCohesion).

   So whenever we come across a $\mathbf{\Pi}$, we should replace it by ʃ, right? E.g., many in this section.

3. • CommentRowNumber3.
   • CommentAuthorUrs
   • CommentTimeJan 7th 2013
   • PermaLink
   Author: Urs
   Format: MarkdownItexMaybe for the time being we can just state that ʃ is to be read synonymously with $\mathbf{\Pi}$, with the former potentially preferred in type theory, while the latter potentially preferred from the point of view of algebraic topology.

   Maybe for the time being we can just state that ʃ is to be read synonymously with $\mathbf{\Pi}$, with the former potentially preferred in type theory, while the latter potentially preferred from the point of view of algebraic topology.

4. • CommentRowNumber4.
   • CommentAuthorMike Shulman
   • CommentTimeJan 7th 2013
   • PermaLink
   Author: Mike Shulman
   Format: MarkdownItexDid we settle on ʃ? I thought there was some argument that the potential for confusion with an integral sign was undesirable. I kind of like $$$.

   Did we settle on ʃ? I thought there was some argument that the potential for confusion with an integral sign was undesirable. I kind of like $$$.

5. • CommentRowNumber5.
   • CommentAuthorUrs
   • CommentTimeJan 7th 2013
   • PermaLink
   Author: Urs
   Format: MarkdownItexYou have to decide. To me the similarity of $\prod$ with $\mathbf{\Pi}$ seems to be of the same sort of that of $\int$ with ʃ. I am happy to live with both. The symbol "$" seems to raise the wrong associations in me, but I guess I can get used to it. What is not practical for me (if that was suggested above, maybe) is to go and change all the numerous occurences of $\mathbf{\Pi}$ in all $n$Lab entries, all my published articles and all my preprints. Nor does it seem desireable to me. I am happy with telling the reader at the beginning of each context which notation it should be.

   You have to decide. To me the similarity of $\prod$ with $\mathbf{\Pi}$ seems to be of the same sort of that of $\int$ with ʃ. I am happy to live with both.

   The symbol “$” seems to raise the wrong associations in me, but I guess I can get used to it.

   What is not practical for me (if that was suggested above, maybe) is to go and change all the numerous occurences of $\mathbf{\Pi}$ in all $n$Lab entries, all my published articles and all my preprints. Nor does it seem desireable to me.

   I am happy with telling the reader at the beginning of each context which notation it should be.

6. • CommentRowNumber6.
   • CommentAuthorTodd_Trimble
   • CommentTimeJan 7th 2013
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   Author: Todd_Trimble
   Format: MarkdownItexFWIW, I don't like $ that much, and like the integral-looking thing more (although I don't know how to type it). I'd always feel $ was some LaTeX typo.

   FWIW, I don’t like $ that much, and like the integral-looking thing more (although I don’t know how to type it). I’d always feel $ was some LaTeX typo.

7. • CommentRowNumber7.
   • CommentAuthorUrs
   • CommentTimeJan 7th 2013
   • PermaLink
   Author: Urs
   Format: MarkdownItex> (although I don’t know how to type it) see [here](http://nforum.mathforge.org/discussion/4594/shape-modality-flat-modality-sharp-modality/?Focus=37694#Comment_37694) > I’d always feel $ was some LaTeX typo. Yes, that's my first association, too. But I suppose I could get used to it.

   (although I don’t know how to type it)

   see here

   I’d always feel $ was some LaTeX typo.

   Yes, that’s my first association, too. But I suppose I could get used to it.

8. • CommentRowNumber8.
   • CommentAuthorMike Shulman
   • CommentTimeJan 8th 2013
   • PermaLink
   Author: Mike Shulman
   Format: MarkdownItexI think it's a shame if the use of \$ in LaTeX means that we can't ever also use it in mathematics. LaTeX uses % for comments, but we still feel free to use it for percentages. (-: And it seems unlikely to me that a LaTeX typo would ever actually produce a file which compiled and yet contained some \$ characters in the output. But I guess two data points suggests that more other mathematicians would also feel uncomfortable with it.

   I think it’s a shame if the use of $ in LaTeX means that we can’t ever also use it in mathematics. LaTeX uses % for comments, but we still feel free to use it for percentages. (-: And it seems unlikely to me that a LaTeX typo would ever actually produce a file which compiled and yet contained some $ characters in the output. But I guess two data points suggests that more other mathematicians would also feel uncomfortable with it.

9. • CommentRowNumber9.
   • CommentAuthorUrs
   • CommentTimeJan 8th 2013
   • (edited Jan 8th 2013)
   • PermaLink
   Author: Urs
   Format: MarkdownItexBut is there really an issue with "ʃ" ? To the extent that people think of ʃ$ X$ as being "integral over $X$" where $X$ is a type, it actually makes sense: it can be thought of as the homotopy coend over $X$ thought of as a simplicial object. So the only sensible interpretatin of ʃ$ X$ as an "integral over $X$" is actually the intended interpretation! So that's good, not a problem. I'd think.

   But is there really an issue with “ʃ” ? To the extent that people think of ʃ$X$ as being “integral over $X$” where $X$ is a type, it actually makes sense: it can be thought of as the homotopy coend over $X$ thought of as a simplicial object. So the only sensible interpretatin of ʃ$X$ as an “integral over $X$” is actually the intended interpretation! So that’s good, not a problem.

   I’d think.

10. • CommentRowNumber10.
    • CommentAuthorMike Shulman
    • CommentTimeJan 8th 2013
    • PermaLink
    Author: Mike Shulman
    Format: MarkdownItexIf you don't think there's a problem with ʃ, I'm okay with it. I guess in other contexts you would be integrating a *function* rather than a *type*. Okay, let's go with ʃ. Would you object if someone else happened to change $\mathbf{\Pi}$s to ʃs in an nLab page? I'm not planning to go through the whole nLab either, but if I happen to be editing some page anyway, I might want to make it consistent.

    If you don’t think there’s a problem with ʃ, I’m okay with it. I guess in other contexts you would be integrating a function rather than a type. Okay, let’s go with ʃ.

    Would you object if someone else happened to change $\mathbf{\Pi}$s to ʃs in an nLab page? I’m not planning to go through the whole nLab either, but if I happen to be editing some page anyway, I might want to make it consistent.

11. • CommentRowNumber11.
    • CommentAuthorUrs
    • CommentTimeJan 8th 2013
    • PermaLink
    Author: Urs
    Format: MarkdownItexOkay, good, yes! And I am fine with changing $\mathbf{\Pi}$s to ʃ, yes. I just feel overwhelmed with doing it globally and consistently. (One fine day we might have $n$Lab-wide macros...)

    Okay, good, yes!

    And I am fine with changing $\mathbf{\Pi}$s to ʃ, yes. I just feel overwhelmed with doing it globally and consistently.

    (One fine day we might have $n$Lab-wide macros…)

12. • CommentRowNumber12.
    • CommentAuthorMike Shulman
    • CommentTimeJan 9th 2013
    • PermaLink
    Author: Mike Shulman
    Format: MarkdownItex(That would be pretty cool.)

    (That would be pretty cool.)