Kerodon

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Comments on Proposition 3.3.4.8

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Comment #2382 by Manuel Araújo on

"In fact, we will show that the map Fun (X, Q) → Fun (Sd (X), Q) is a weak homotopy equivalence".

If I'm not mistaken, the proof actually shows directly that Fun (X, Q) → Fun (Sd (X), Q) is a homotopy equivalence.

Comment #2385 by Kerodon on

Yep (of course it is automatic, since it is a map of Kan complexes.)

Comment #2817 by Weilong ZHAO on

Little typo: I think the range of should be .

Moreover, to apply Proposition 00XC, we need to prove that the vertical maps in the first commutative square are Kan fibrations, i.e. is injective.

There are also:

  • 5 comment(s) on Chapter 3: Kan Complexes
  • 4 comment(s) on Section 3.3: The $\operatorname{Ex}^{\infty }$ Functor

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