Kerodon

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Comments on Subsection 1.1.2

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Comment #35 by Daniel on

"Example 1.1.2.13. The horn coincides with the -simplex ."

Should really be defined for ? Also, strictly following construction 1.1.2.9, we would have .

Comment #36 by Daniel on

[Typo:] In Exercise 1.1.2.14: ""

Comment #45 by Kerodon on

Oops; that's right, the horn of the 0-simplex should be empty. Thanks!

Comment #285 by Stephen L on

So I guess the idea is that though normally (coming from traditional geometry) a simplex is identified only with all faces/edges/points/etc. contained in it, here a standard n-simplex consists of all things that can be embedded in it, included ways of collapsing higher-dimensional simplices onto it. That's a lot of extra parts! Interesting to see where this goes as I read further....

Comment #286 by Stephen L on

Wait, I got it backwards. is can be thought of as "ways of embedding an n simplex in other simplices". And so the yoneda statement is something like

"a way of going from 'generic ways of embedding an n-simplex' to 'a concrete realization of various simplices' is the same as specifying a particular concrete n-simplex . "

(I'm trying to keep my geometric intuition alive as I work through...)

Comment #402 by Nicholas Mertes on

In Construction 1.1.2.9 (The Horn ): A remark should be added explaining that is the subfunctor of generated by the maps . Then it would be more clear why a morphism of simplicial sets can be determined by saying where sends the generators .

There are also:

  • 11 comment(s) on Chapter 1: The Language of $\infty $-Categories
  • 7 comment(s) on Section 1.1: Simplicial Sets

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