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1. • CommentRowNumber1.
   • CommentAuthormaxsnew
   • CommentTimeOct 10th 2022
   • PermaLink
   Author: maxsnew
   Format: MarkdownItexclarify that polarity is about all universal properties, not just limits/colimits, and talk a bit about why it makes sense for a type to have "both polarities" <a href="https://ncatlab.org/nlab/revision/diff/polarity+in+type+theory/6">diff</a>, <a href="https://ncatlab.org/nlab/revision/polarity+in+type+theory/6">v6</a>, <a href="https://ncatlab.org/nlab/show/polarity+in+type+theory">current</a>

   clarify that polarity is about all universal properties, not just limits/colimits, and talk a bit about why it makes sense for a type to have “both polarities”

   diff, v6, current

2. • CommentRowNumber2.
   • CommentAuthorGuest
   • CommentTimeOct 10th 2022
   • PermaLink
   Author: Guest
   Format: MarkdownItexWhat's the (infinity, 1)-categorical version of a representable functor? Because in certain models of type theory such as homotopy type theory I'd imagine the 'representable functors' to actually be $C \to \infty\mathrm{Grpd}$ or $C^\op \to \infty\mathrm{Grpd}$ rather than $C \to \mathrm{Set}$ and $C^\op \to \mathrm{Set}$

   What’s the (infinity, 1)-categorical version of a representable functor? Because in certain models of type theory such as homotopy type theory I’d imagine the ’representable functors’ to actually be $C \to \infty\mathrm{Grpd}$ or $C^\op \to \infty\mathrm{Grpd}$ rather than $C \to \mathrm{Set}$ and $C^\op \to \mathrm{Set}$

3. • CommentRowNumber3.
   • CommentAuthorMike Shulman
   • CommentTimeOct 11th 2022
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   Author: Mike Shulman
   Format: MarkdownItexYes, the $(\infty,1)$-categorical representable functors land in $\infty Gpd$.

   Yes, the $(\infty,1)$-categorical representable functors land in $\infty Gpd$.

4. • CommentRowNumber4.
   • CommentAuthorMike Shulman
   • CommentTimeOct 11th 2022
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   Author: Mike Shulman
   Format: MarkdownItexSee [[(∞,1)-category of (∞,1)-presheaves]], [[Yoneda lemma for (infinity,1)-categories]].

   See (∞,1)-category of (∞,1)-presheaves, Yoneda lemma for (infinity,1)-categories.

5. • CommentRowNumber5.
   • CommentAuthorUrs
   • CommentTimeDec 17th 2022
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   Author: Urs
   Format: MarkdownItexI have streamlined some wording in this entry and added a bunch of further hyperlinks (such as to *[[term elimination]]*, etc.) I notice that a lot of entries (such as this one) are requesting links to *[[call-by-name]]* and/or to *[[call-by-value]]*, while these links remain broken. Would it be hard to create these entries with some minimum content? <a href="https://ncatlab.org/nlab/revision/diff/polarity+in+type+theory/8">diff</a>, <a href="https://ncatlab.org/nlab/revision/polarity+in+type+theory/8">v8</a>, <a href="https://ncatlab.org/nlab/show/polarity+in+type+theory">current</a>

   I have streamlined some wording in this entry and added a bunch of further hyperlinks (such as to term elimination, etc.)

   I notice that a lot of entries (such as this one) are requesting links to call-by-name and/or to call-by-value, while these links remain broken. Would it be hard to create these entries with some minimum content?

   diff, v8, current