nForum - Discussion Feed (Comma category in the Pointwise by Conical Limits section of Kan extension)2022-01-25T18:14:42-05:00https://nforum.ncatlab.org/
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Zhen Lin comments on "Comma category in the Pointwise by Conical Limits section of Kan extension" (43539)https://nforum.ncatlab.org/discussion/5508/?Focus=43539#Comment_435392013-11-25T22:04:38-05:002022-01-25T18:14:42-05:00Zhen Linhttps://nforum.ncatlab.org/account/318/
It’s not really a (co)slice category. As you surmised, the domain of Δ c′\Delta_{c'} is indeed 𝟙\mathbb{1}, and the description as a comma category is completely accurate.

It’s not really a (co)slice category. As you surmised, the domain of $\Delta_{c'}$ is indeed $\mathbb{1}$, and the description as a comma category is completely accurate.

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JasonGross comments on "Comma category in the Pointwise by Conical Limits section of Kan extension" (43537)https://nforum.ncatlab.org/discussion/5508/?Focus=43537#Comment_435372013-11-25T21:45:06-05:002022-01-25T18:14:42-05:00JasonGrosshttps://nforum.ncatlab.org/account/923/
What's the indexing category of the constant diagram functor used in http://ncatlab.org/nlab/show/Kan+extension#PointwiseByConicalLimits (that is, what is the domain category of Δ_{c'})? I suspect ...
What's the indexing category of the constant diagram functor used in http://ncatlab.org/nlab/show/Kan+extension#PointwiseByConicalLimits (that is, what is the domain category of Δ_{c'})? I suspect it's the terminal category, in which case I'm confused why the notation Δ_{c'} / p rather than just c' / p is being used. Either way, I think that part of the page needs a clarification (either replacing Δ_{c'} with c' and saying that it's a (co)slice category, or mentioning what the indexing category is for the constant diagram functor.)
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