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Vanilla 1.1.10 is a product of Lussumo. More Information: Documentation, Community Support.
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You mean page 42 of the published book pdf, page 30 of the arXiv version (I like to look at the arXiv version, as that is fully hyper-cross linked, without that I find the book too large to read).
I think the notation means literally the powering of the simplicial set by the set , equivalently the internal hom by the latter, regarded as a discrete simplicial set. So this is equivalently just the cartesian product of (n-1)-copies, hence a cube, in this sense.
If we believe the analysis that the left vertical map in question is hence the incusion of the boundary of the cube minus one of its faces into the cube, then this is clearly an acyclic cofibration and hence anodyne.
(Or so I think, let me know if I sound like I am mixed up.)
I looked for a book review of HTT but couldn’t find one. Is there any?
I thought there was a MathSciNet review. But maybe I am hallucinating. I cannot check myself right now.
There is a MathSciNet review: MR2522659
Thanks. Unfortunately these are always absurdly complicated to access via my affiliated library…
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