Timeline for Non-degenerate simplexes in a Kan complex
Current License: CC BY-SA 4.0
7 events
| when toggle format | what | by | license | comment | |
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| Jul 25, 2020 at 21:08 | comment | added | nrkm | I just meant your $C$ is equivalent to a point (which uses the fact that it is a homotopy pushout by left properness). I see you had a bit more direct way of saying it (they’re more or less the same). But I just wanted to say that (weak equivalence+monomorphism)$\Leftrightarrow$(LLP w.r.t. Kan fibrations) is in a “less trivial tier” than this exercise, so I still prefer to prove directly (and it’s intuitively pretty clear how to attach cells, writing it down is somewhat cumbersome, though). | |
| Jul 25, 2020 at 15:57 | comment | added | Lao-tzu | I don't quite know what you are speaking but I wrote an answer below where you can see my argument (better to draw more commutative diagrams to see some identities I claimed). Hope to be useful for others. | |
| Jul 25, 2020 at 15:16 | comment | added | nrkm | You’re right, fixed. It took some time to understand your argument, but you mean “it’s enough to prove the map is an trivial cofibration. Cofibration because it’s an inclusion, weak equivalence because everything is weakly contractible?” (my argument is still very easy, drew a picture and only used the definition :) | |
| Jul 25, 2020 at 15:04 | history | edited | nrkm | CC BY-SA 4.0 |
fixed typo
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| Jul 25, 2020 at 13:53 | comment | added | Lao-tzu | Thanks for your answer and thanks @Tom Goodwillie for your idea! Just one comment: the correct formula (in my opinion) should be $f' = s_{n-1}d_n f$, and in showing $i$ to be anodyne, it will be much easier by drawing commutative diagrams, and using properness and 2-out-of-3 properties. | |
| Jul 25, 2020 at 13:50 | vote | accept | Lao-tzu | ||
| Jul 24, 2020 at 19:33 | history | answered | nrkm | CC BY-SA 4.0 |