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• CommentRowNumber1.
• CommentAuthorJasonGross
• CommentTimeNov 25th 2013
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.)
• CommentRowNumber2.
• CommentAuthorZhen Lin
• CommentTimeNov 25th 2013

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.